While I cannot find an out of universe explanation, the code is an exact copy of the one from TOS Let That Be Your Last Battlefield as indicated by @Buzz in the comments. The only difference is who speaks the words.
A transcript of TOS:LTBYLB shows the following, which also indicates that besides the code, voice recognition is used (So any phrase would work, like "monkey monkey football" or similar):
KIRK: Computer, destruct sequence. Are you ready to copy?
KIRK: Prepare to verify destruct sequence code one. Computer, this is Captain James Kirk of the USS Enterprise. Destruct sequence one, code one, one A.
COMPUTER Voice and code one, one A verified and correct. Sequence one complete.
KIRK: Mister Spock.
SPOCK: This is Commander Spock, science officer. Destruct sequence number two, code one, one A, two B.
COMPUTER: Voice and code verified and correct. Sequence two complete.
KIRK: Mister Scott.
SCOTT: This is Lieutenant Commander Scott, chief engineering officer of the USS Enterprise. Destruct sequence number three, code one B, two B, three.
COMPUTER: Voice and code one B, two B, three verified and correct. Destruct sequence completed and engaged. Awaiting final code for thirty second countdown.
KIRK: Mister Spock, has the ship returned to the course set for it by my orders?
SPOCK: Negative, Captain. We are still headed directly for Cheron.
COMPUTER: Destruct sequence engaged. Awaiting final code for thirty second countdown.
KIRK: Computer, this is Captain James Kirk of the USS Enterprise. Begin thirty second countdown. Code zero, zero, zero, destruct zero.