Upvote:4
According to Timatic:
Korea (Rep. of), South - Destination Visa
Visa required.
The following are exempt from holding a visa:
Nationals of Kazakhstan with a normal passport for a maximum stay of 30 days.
Thus you don't need a visa for this. Note that there's also a hotel in the airport itself, which might be more comfortable if you have an early flight.
Note that the trains to airport do not run at night; as far as I remember, there are no trains between midnight and 5:30am.