The generator matrix

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

generates a code of length 30 over GR(16,4) who´s minimum homogenous weight is 81.

Homogenous weight enumerator: w(x)=1x^0+168x^81+96x^82+180x^83+87x^84+492x^85+204x^86+168x^87+78x^88+540x^89+156x^90+144x^91+36x^92+804x^93+228x^94+216x^95+21x^96+300x^97+84x^98+60x^99+6x^100+6x^104+12x^108+6x^112+3x^116

The gray image is a code over GF(4) with n=120, k=6 and d=81.
This code was found by Heurico 1.16 in 1.7 seconds.