The generator matrix

 1  0  0  1  1
 0  1  0  1  a
 0  0  1 3a+3  a

generates a code of length 5 over GR(16,4) who´s minimum homogenous weight is 9.

Homogenous weight enumerator: w(x)=1x^0+120x^9+270x^12+720x^13+1152x^15+735x^16+1080x^17+18x^20

The gray image is a code over GF(4) with n=20, k=6 and d=9.
This code was found by Heurico 1.16 in 1.01e-007 seconds.