The generator matrix

 1  1  1  1
 0 12  8  4

generates a code of length 4 over Z16 who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+62x^4+1x^8

The gray image is a code over GF(2) with n=32, k=6 and d=16.
This code was found by Heurico 1.16 in 7.61e-005 seconds.