The generator matrix

 1  1  2  1
 0 12 12  0
 0  0  8  0

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

Homogenous weight enumerator: w(x)=1x^0+6x^2+16x^3+82x^4+16x^5+6x^6+1x^8

The gray image is a code over GF(2) with n=32, k=7 and d=8.
This code was found by Heurico 1.16 in 6.29e-005 seconds.