Earlier quoted context omitted.
mikegerwitz is technically right. As an illuminating example, consider a hash-algorithm in which there's at least one hash that occurs precisely once. Then a 2nd-preimage attack is formally impossible no matter how much computational power you have (assuming by "second" you meant "distinct second"). But a 1st-preimage attack is formally possible.
One of the requirements for a hash to be cryptographically secure is that all possible values are equally likely. So yes, it is possible (in fact trivial) to construct a hash of the sort you describe, but such a hash would not be cryptographically secure to begin with.
I'd be willing to bet that an altered version of SHA3-256 that replaces four bits in the middle with length%16 is better for most purposes than SHA256, despite being non-uniform.