Fast way to find a matrix with only $0$ and $1$ as entries full-rank or not?

Fast way to find a matrix with only $0$ and $1$ as entries full-rank or not?

I have a huge number of small Zero-One Matrices($4\times 4$,
$5\times5$,$6\times6$) and I want to determine whether they are full-rank
or not one by one.
Gaussian elimination is a option, I want to know is there any faster way
since only $1$s and $0$s in the matrices.