The generator matrix

 1  1  2  2
 0  2  2  8
 0  0  4  4
 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+52x^2+160x^3+598x^4+160x^5+52x^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 0.000211 seconds.