The generator matrix

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

generates a code of length 34 over GR(16,4) who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+225x^84+297x^88+474x^92+192x^93+543x^96+1728x^97+522x^100+5184x^101+504x^104+5184x^105+528x^108+480x^112+309x^116+159x^120+54x^124

The gray image is a code over GF(4) with n=136, k=7 and d=84.
This code was found by Heurico 1.16 in 1.8 seconds.