The generator matrix

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

generates a code of length 8 over GR(16,4) who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+96x^22+60x^24+96x^26+3x^32

The gray image is a code over GF(4) with n=32, k=4 and d=22.
This code was found by Heurico 1.16 in 3.24e-008 seconds.