The generator matrix

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

generates a code of length 5 over GR(16,4) who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+270x^12+735x^16+18x^20

The gray image is a code over GF(4) with n=20, k=5 and d=12.
This code was found by Heurico 1.16 in 1.01e-007 seconds.