The generator matrix

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

generates a code of length 31 over GR(16,4) who´s minimum homogenous weight is 77.

Homogenous weight enumerator: w(x)=1x^0+156x^77+516x^78+564x^79+1125x^80+1116x^81+4080x^82+2016x^83+4140x^84+5040x^85+11052x^86+5148x^87+10533x^88+11448x^89+22080x^90+9408x^91+20337x^92+22524x^93+32028x^94+11340x^95+21045x^96+16812x^97+23184x^98+7200x^99+7698x^100+4344x^101+5364x^102+1188x^103+552x^104+60x^108+21x^112+18x^116+3x^120+3x^124

The gray image is a code over GF(4) with n=124, k=9 and d=77.
This code was found by Heurico 1.16 in 96 seconds.