The generator matrix

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

generates a code of length 31 over GR(16,4) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+987x^80+4704x^84+10449x^88+20016x^92+20181x^96+8688x^100+444x^104+63x^112+3x^120

The gray image is a code over GF(4) with n=124, k=8 and d=80.
This code was found by Heurico 1.16 in 86.3 seconds.