Enlightend beings don't make more good or neutral karma?

If you understand by karma to simply mean causation (of some kind) then karma is there, irrespective of whether one is enlightened or not. If you understand by karma as action (at any of the three levels of body, speech or mind) then karma is there, irrespective of whether one is enlightened or not.

The way karma is different is only in the sense of being good or bad karma. A good karma means action that does not lead to further clinging, a cause whose effect is as benficial as the unclinging cause is. A bad karma means action that creates clinging, a causae whose effect is harmful, as one becomes clings slightly strongly than before to the samsaric flow.

Karma comes as a result dependent on conditions. If conditions are right, then the result will arise, endure and cease. If conditions are not right, then the result will not arise, not endure and not cease. The arising (and enduring and ceasation) of every karmic action (and karmic intention) is inevitable. That is, karma is bound to produce some effects, results, consequences; irrespective of the fact that it is the karma of enlightened being or not an enlightened being.

As one builds up more good karma, it becomes easier to build up more good karma even further (habituation, conditioning).

If by enlightened karma, you mean the karma of enlightened beings, then certainly all of it is good- for by very definition of enlightened beings, all there actions, words and thoughts are steeped in wisdom and compassion.

As I see it dukkha or suffering is bad karma, good karma leads to nirvana. And when all karma is purified Nirvana happens.

If all karma is purified then it's not possible to create bad karma because every thought and action is purified and is Nirvana.

Nirvana is having no bad karma and if that is the case then all actions are good karma for all sentient beings.

Buddha spoke about cessation of karma and liberation from karma. For Arahant, or for Buddha, there's no acquiring of karma anymore. Indeed, if they still acquired karma, how could we call it "liberation"?

But how can an Arahant or a Buddha act without acquiring karma?

In my understanding, this is possible because only appropriated action, i.e. action considered to be done "by me" counts as that person's own karma.

Since an enlightened being does not reify the concept of "a being" or "self", there is no-one left to acquire karma. There is no way Buddha could appropriate his actions as "I did this", because he had done away with the notion of "I", he only used it for communication with the unenlightened.

So whatever we think is done by Buddha or Arahant, from their perspective is not their (personal) intention, and is therefore not their (personal) karma.

Buddha's actions can still have results. Generally speaking, in terms of results, this is the third type of actions, one that leads to cessation. We can still observe some of the results of Buddha's actions in our own lives - us studying and practicing Dharma. In fact, the results are unfolding in front of our own eyes, in form of this question and answer site. But these results are not Buddha's personal karma, since they did not come bundled with the concept of "self".

The outcome of deeds is discussed in AN4.233:

“Mendicants, I declare these four kinds of deeds, having realized them with my own insight.

What four?

There are dark deeds with dark results;

bright deeds with bright results;

dark and bright deeds with dark and bright results; and

neither dark nor bright deeds with neither dark nor bright results, which lead to the ending of deeds.

The fourth is the destination of the Noble Eightfold Path:

And what are neither dark nor bright deeds with neither dark nor bright results, which lead to the ending of deeds? It’s the intention to give up dark deeds with dark results, bright deeds with bright results, and both dark and bright deeds with both dark and bright results. These are called neither dark nor bright deeds with neither dark nor bright results, which lead to the ending of deeds. These are the four kinds of deeds that I declare, having realized them with my own insight.”

In other words, in giving up identity view and all its wishes, the grasping that leads to rebirth, continued existence and suffering is relinquished and extinguished.

Note that non-arahants with some attainment as well as arahants would both relinquish the first three deeds in favor of the fourth. The difference is that non-arahants would still wish and need to practice towards the realization of the fourth clause. They would still have some identity view (e.g., "the conceit, 'I am'").

With Right Wisdom and Right Freedom, arahants will have given up all deeds. Arahants will, per this sutta, have attained the "ending of deeds".

In its essence, "kamma" means "action" with attachment.

While the suttas do refer to "kamma without attachment" namely, "neither-dark-nor-bright kamma" (AN 4.237), this type of kamma is also called the "kamma that ends kamma" (AN 6.63). Therefore, it is not really "kamma".

the essential meaning of "kamma" is "action with attachment", as follows:

And what is the right view with effluents, siding with merit, resulting in acquisitions (attachment)? 'There is what is given, what is offered, what is sacrificed. There are fruits & results of good & bad actions....

MN 117

Refer to Bhikkhu Buddhadasa PDF booklet: Kamma in Buddhism