The most important families of non-linear codes are systematic. A brute-force
check is the only known method to compute their weight distribution and
distance distribution. On the other hand, it outputs also all closest word
pairs in the code. In the black-box complexity model, the check is optimal
among closest-pair algorithms. In this paper we provide a Groebner basis
technique to compute the weight/distance distribution of any systematic
non-linear code. Also our technique outputs all closest pairs. Unlike the
check, our method can be extended to work on code families.