The generator matrix

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

generates a code of length 31 over GR(16,4) who´s minimum homogenous weight is 83.

Homogenous weight enumerator: w(x)=1x^0+252x^83+525x^84+540x^85+96x^86+936x^87+1206x^88+816x^89+192x^90+1440x^91+1809x^92+1032x^93+288x^94+1512x^95+1905x^96+1008x^97+192x^98+1092x^99+915x^100+444x^101+144x^103+18x^104+15x^108+6x^112

The gray image is a code over GF(4) with n=124, k=7 and d=83.
This code was found by Heurico 1.16 in 0.548 seconds.