The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+120x^6+30x^8+960x^9+1080x^10+6780x^12+5760x^13+3240x^14+15360x^15+20265x^16+8640x^17+3240x^18+60x^20

The gray image is a code over GF(4) with n=20, k=8 and d=6.
This code was found by Heurico 1.16 in 0.218 seconds.