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

generates a code of length 31 over GR(16,4) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+264x^76+378x^80+459x^84+768x^87+387x^88+4608x^91+711x^92+6912x^95+540x^96+573x^100+393x^104+285x^108+93x^112+12x^116

The gray image is a code over GF(4) with n=124, k=7 and d=76.
This code was found by Heurico 1.16 in 25.8 seconds.