There are no secret or hidden levels in PSX Final Doom; and
subsequently there are no "secret" exits, per se.

Level 23, BALLISTYX, has 2 exits, one that is accessible in
Single-player and Cooperative games, the other exit (just
outside of a caged area which overlooks a walled-in field
of short pillars) is accessible only in Deathmatch games...
What you're seeing is the Deathmatch exit.  (In Deathmatch
games only this outside part of the map is accessible.)

Both exits lead to level 24, HECK.

For more information including maps and screenshots, access
http://classicdoom.com/bal-dmx.htm

--Led

www.ClassicDOOM.com
Support for console and PC Classic Doom games