The generator matrix

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

generates a code of length 31 over GR(16,4) who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+141x^84+192x^85+96x^86+405x^88+396x^89+192x^90+426x^92+348x^93+288x^94+549x^96+420x^97+192x^98+240x^100+180x^101+12x^104+6x^108+6x^112+3x^116+3x^120

The gray image is a code over GF(4) with n=124, k=6 and d=84.
This code was found by Heurico 1.16 in 0.0414 seconds.