The generator matrix

 1  0  0  1
 0  1  0  2
 0  0  1  2

generates a code of length 4 over Z16 who´s minimum homogenous weight is 2.

Homogenous weight enumerator: w(x)=1x^0+92x^2+640x^3+2630x^4+640x^5+92x^6+1x^8

The gray image is a code over GF(2) with n=32, k=12 and d=8.
This code was found by Heurico 1.16 in -8.39e-008 seconds.