The generator matrix

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

generates a code of length 5 over Z16 who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+24x^4+80x^5+20x^6+3x^8

The gray image is a code over GF(2) with n=40, k=7 and d=16.
This code was found by Heurico 1.16 in 0.000194 seconds.