The generator matrix

 1  1  1  1
 0  2 12  6

generates a code of length 4 over Z16 who´s minimum homogenous weight is 3.

Homogenous weight enumerator: w(x)=1x^0+16x^3+94x^4+16x^5+1x^8

The gray image is a code over GF(2) with n=32, k=7 and d=12.
This code was found by Heurico 1.16 in 7.58e-005 seconds.