The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  2  1  1  1
 0  2  0  0  0  0  2  2  2 2a  2 2a+2  0 2a 2a+2 2a  0 2a  2  2  0  2 2a+2 2a 2a  0  2  2  2 2a  0
 0  0  2  0  0  2 2a+2 2a 2a 2a  2  0  2 2a+2 2a  0 2a 2a+2  2  2  2  2  0  0  0  2  2  0 2a 2a 2a
 0  0  0  2  0 2a+2  0  2 2a 2a 2a 2a+2 2a  0 2a  2  0  2  2 2a 2a  0  0 2a+2  2 2a+2 2a+2  2 2a+2  2  2
 0  0  0  0  2  2  2 2a+2  2  0 2a+2 2a  0 2a+2  0 2a  2 2a+2  2  2 2a 2a+2  2 2a+2  0 2a  0  0 2a+2  0  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+93x^80+186x^84+192x^87+183x^88+1152x^91+117x^92+1728x^95+147x^96+105x^100+78x^104+63x^108+39x^112+9x^116+3x^120

The gray image is a code over GF(4) with n=124, k=6 and d=80.
This code was found by Heurico 1.16 in 0.0798 seconds.