The generator matrix

 1  0  0  1
 0  1  0  1
 0  0  1  1
 0  0  0  8

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

Homogenous weight enumerator: w(x)=1x^0+172x^2+1344x^3+5158x^4+1344x^5+172x^6+1x^8

The gray image is a code over GF(2) with n=32, k=13 and d=8.
This code was found by Heurico 1.16 in 0.015 seconds.