This article is from the Final-Fantasy and other Square Soft Games FAQ, by firstname.lastname@example.org (Nick Zitzmann) with numerous contributions by others.
It's on Floor 19 of the Tower. Somewhere on this level is a little room
with corpses littering the floor. Take the stairs, and you'll find a
dead corpse and his diary. Read the diary, and you get the Nuke Bomb -
the game's most powerful weapon. (Note that the item is added to your
inventory without notifying you.)
The diary also contains an extremely important clue about the forces
controlling Ashura, so read it carefully.