Ok since the code is the same thing for all players and in order to get the code you need to finish the game the code:

62131

Endless mode allows you to play one of three game types with an endless flow of procedurally-generated entrants: Timed, Perfection, or Endurance. Each game type has a different scoring system. You can also choose from four different rule sets for any game type.

Endless mode is unlocked by entering a five-digit code which is unlocked after reaching ending 20 in story mode. The same code is shared among all copies of the game and is not generated separately for each player or playthrough.

* Took this from Papers, Please Wiki page.