The curious case here is how much of a description do we give it of itself? That would almost certainly dominate success rates.
My feeling is that a prompt would have to provide a vague description of a program that meaningfully passes something like a Turing test, an API to conform to, an expectation of novel construction (no 'ifs all the way down'), and then a requirement to search broadly and pursue promising ideas and not get hung up on the philosophy. Anything more precise feels like it would corrupt the test, but as it is that description feels doomed to loop before even trying the interesting parts.
I wonder if we could just tell it to invent itself without any description and see if it can I introspect enough through its own interface to figure out what it is.