The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+30x^16+144x^18+60x^20+384x^21+864x^22+60x^24+1152x^25+1296x^26+84x^28+21x^32

The gray image is a code over GF(4) with n=32, k=6 and d=16.
This code was found by Heurico 1.16 in 0.0042 seconds.