The generator matrix

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

generates a code of length 32 over GR(16,4) who´s minimum homogenous weight is 83.

Homogenous weight enumerator: w(x)=1x^0+276x^83+414x^84+420x^85+1152x^86+1632x^87+1626x^88+1440x^89+2832x^90+3408x^91+3081x^92+2496x^93+4344x^94+5448x^95+5145x^96+3000x^97+6264x^98+6204x^99+4674x^100+2844x^101+3432x^102+2712x^103+1422x^104+552x^105+408x^106+288x^107+9x^108+6x^112+6x^116

The gray image is a code over GF(4) with n=128, k=8 and d=83.
This code was found by Heurico 1.16 in 7.7 seconds.