The generator matrix

 1  0  1  1
 0  1  3  6

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

Homogenous weight enumerator: w(x)=1x^0+52x^3+149x^4+52x^5+2x^6

The gray image is a code over GF(2) with n=32, k=8 and d=12.
This code was found by Heurico 1.16 in 7.41e-005 seconds.