The generator matrix

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

generates a code of length 32 over GR(16,4) who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+108x^82+252x^83+909x^84+240x^85+708x^86+1392x^87+2580x^88+672x^89+1620x^90+3072x^91+5619x^92+1344x^93+3336x^94+5184x^95+9054x^96+2208x^97+3828x^98+5916x^99+7800x^100+1488x^101+2388x^102+2544x^103+2538x^104+192x^105+300x^106+72x^107+87x^108+39x^112+33x^116+12x^120

The gray image is a code over GF(4) with n=128, k=8 and d=82.
This code was found by Heurico 1.16 in 27.1 seconds.