The generator matrix

 1  0  0  1  1
 0  1  0  1  0
 0  0  1 3a+3  0
 0  0  0  2 2a

generates a code of length 5 over GR(16,4) who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+36x^6+30x^8+240x^9+324x^10+1212x^12+1440x^13+972x^14+5376x^15+3561x^16+2160x^17+972x^18+60x^20

The gray image is a code over GF(4) with n=20, k=7 and d=6.
This code was found by Heurico 1.16 in 0.016 seconds.