Counting the number of $3\times 4$ matrices with all entries either $0$ or $1$ such that no row/column contains all $0$'s

Question

Problem:

How many $3\times 4$ matrices are there with all entries either $0$ or $1$ such that there is no row or column which contains all $0$'s?

I have tried the problem using inclusion-exclusion principle but it is becoming very complicated. I started with $2^{12}$ total possibilities, then while subtracting the terms, it is becoming complicated.

Any help would be appreciated!