The generator matrix

 1  0  0  0  1  1  1  2  1  1  1  1  1  1  1  1 2a+2  1  1  1  1  1  1  0  1  1  1  1 2a+2  1  1
 0  1  0  0  2  1  3  1  a 3a+3 3a  1 2a+3 a+1 3a+3 3a+1  1 2a+1 3a+2 2a+1  a 2a 2a+2 2a  0 2a  0 3a+3  1 a+3 2a+2
 0  0  1  0 2a+3  1 2a+2 2a+3 3a+2  a 2a+2 2a+1 3a+1 2a+3 a+2 2a  a 3a 3a+3 a+2  0 a+1  a  1 3a+2 2a a+3 2a+3  2 2a  1
 0  0  0  1 3a+3  2 3a+1 3a+1 2a+2 2a+1 a+1 2a+3 3a+1 a+3 2a+2  2 a+1 3a a+1  0  a 3a+3 a+2 a+3 2a+3 3a+1 a+2  a  1 a+3 3a+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+297x^80+288x^81+492x^82+1104x^83+1554x^84+1272x^85+2028x^86+2484x^87+3216x^88+2796x^89+3372x^90+4116x^91+5313x^92+4428x^93+5052x^94+5772x^95+6315x^96+3876x^97+3768x^98+2892x^99+2508x^100+1164x^101+648x^102+528x^103+240x^104+9x^108+3x^112

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 7.41 seconds.