The lambda calculus (a system we know is capable of infinite self-complexity, learning, etc. with the right program) can be described in a few hundred bits. And a neural net can be described in the lambda calculus in perhaps a few thousand bits.
Also, we have no idea how "compressed" the genome is.
Basic structure can be encoded yes (and obviously is given brains have consistent structure), but the weights or parameters, presuming that brains learn via synaptic weights, obviously do not fit in the genome.
The lambda calculus (a system we know is capable of infinite self-complexity, learning, etc. with the right program) can be described in a few hundred bits. And a neural net can be described in the lambda calculus in perhaps a few thousand bits.
Also, we have no idea how "compressed" the genome is.