The generator matrix

 1  1  1  1
 0  2  0  4
 0  0  2  4

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

Homogenous weight enumerator: w(x)=1x^0+36x^2+96x^3+758x^4+96x^5+36x^6+1x^8

The gray image is a code over GF(2) with n=32, k=10 and d=8.
This code was found by Heurico 1.16 in 0.000197 seconds.