So what's the program? Is it the one that runs every turing machine up to length 100 for BusyBeaver(100) steps, and gets the number BusyBeaver(100) by running the BusyBeaver_100 program whose source code is hardcoded into it? That would be of length 100+c for some constant c, but maybe you didn't think the constant was worth mentioning.
Well, it's still encoded. But I actually meant to say "almost 100" in the original. And yes, that's the answer.
Here's another installment of rationality quotes. The usual rules apply: