The generator matrix

 1  1  1  1  1
 0  2  0  2 2a+2
 0  0  2 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+30x^12+192x^15+15x^16+18x^20

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