The generator matrix

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

generates a code of length 39 over GR(16,4) who´s minimum homogenous weight is 96.

Homogenous weight enumerator: w(x)=1x^0+84x^96+264x^100+366x^104+666x^108+2214x^112+5694x^116+5679x^120+492x^124+456x^128+222x^132+171x^136+54x^140+21x^144

The gray image is a code over GF(4) with n=156, k=7 and d=96.
This code was found by Heurico 1.16 in 1.53 seconds.