The generator matrix

 1  0  1  1  1  1
 0  1  1  a a+1  0
 0  0 2a+2 2a  2  0

generates a code of length 6 over GR(16,4) who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+60x^12+192x^15+21x^16+576x^19+156x^20+18x^24

The gray image is a code over GF(4) with n=24, k=5 and d=12.
This code was found by Heurico 1.16 in 0 seconds.