Student Visa come as a tourist before it expires

can i come as a tourist or do I need to come as a student again?

This is entirely up to the Immigration Officer who lands you (if he does in fact land you). For both cases you will need a convincing reason why you are showing up after your course of study has ended. You can expect to be asked this question during your landing interview and the outcome will depend upon the plausibility of your answer along with your personal impact and articulation skills.

If I come as a tourist I could stay in the UK longer, and if I come as a student I need to leave on June 20. Am i right?

If the IO decides to land you as a visitor, you will be given up to 6 months leave to remain (or a shorter period if the IO thinks it's appropriate). If the IO lands you on the unspent leave of your existing visa, then you will need to be out by midnight 20 June.

If the IO decides not to land you at all, it would be because your explanation (along with other factors) was too weak vis-a-vis the risk of allowing you to enter.

Usually IO's worry when a recent student shows up again, so it's advisable to spend some time thinking about your reason for seeking entry. The only other option that introduces absolute certainty over the IO's impression is to obtain an entry clearance.

It is my recommendation that you enter as a visitor (with a good reason, for example an itinerary and perhaps an invitation letter), not only will that give you more time, but with such little time left on your student visa, it is unlikely that the immigration officer will accept that you are coming into the country as a genuine student for student-related activities. This, while I could not find explicitly in the T4 Migrant Guidelines (official citation added below), has be corroborated across multiple reputable sources, for example:

From Warwick Uni:

... In order to enter the UK using your student visa, you must still meet the requirements of the Immigration Rules for student visas. Students whose studies have ended and who do not intend to take another course when they return to the UK will have difficulties showing that they still meet the requirements of the Immigration Rules for students. If a border force officer considers that your circumstances have changed or that you are attempting to re-enter for a purpose other than that for which your leave was granted, your immigration permission can be cancelled and you can be required to leave the UK or, if you are a non-visa national, you can be granted leave to enter as a visitor instead...

(Please note, even this applies after studies but before graduation. It can be even worse after graduation, for more info, read this article by QMUL)

Further evidence can also be found in Paragraph 321:

321. A person seeking leave to enter the United Kingdom who holds an entry clearance which was duly issued to him and is still current may be refused leave to enter only where the Immigration Officer is satisfied that:

(i) False representations were made or false documents or information were submitted (whether or not material to the application, and whether or not to the holder’s knowledge), or material facts were not disclosed, in relation to the application for entry clearance; or in order to obtain documents from the Secretary of State or a third party required in support of the application.

(ii) a change of circumstances since it was issued has removed the basis of the holder’s claim to admission, except where the change of circumstances amounts solely to the person becoming over age for entry in one of the categories contained in paragraphs 296-316 of these Rules since the issue of the entry clearance; or

(iii) on grounds which would have led to a refusal under paragraphs 320(2), 320(6), 320(18A), 320(18B) or 320(19) (except where this sub-paragraph applies in respect of an entry clearance issued under Appendix Armed Forces it is to be read as if for “paragraphs 320(2), 320(6), 320(18A), 320(18B) or 320(19)” it said “paragraph 8(a), (b), (c) or (g) and paragraph 9(d)”)

And also in paragraph 30A:

30A. An entry clearance may be revoked if the Entry Clearance Officer is satisfied that:

(i) whether or not to the holder’s knowledge, false representations were employed or material facts were not disclosed, either in writing or orally, for the purpose of obtaining the entry clearance; or

(ii) a change of circumstances since the entry clearance was issued has removed the basis of the holder’s claim to be admitted to the United Kingdom, except where the change of circumstances amounts solely to his exceeding the age for entry in one of the categories contained in paragraphs 296-316 of these Rules since the issue of the entry clearance; or

(iii) the holder’s exclusion from the United Kingdom would be conducive to the public good.