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  1  1  1  1  1  2  1  2  1  1  2  2  2  2  1  1  1  1  1  1  2  2  1  1  2  2  2  2  4  0  2  2  4  0  1  1  1  4  8  4  4  8  4  1  2  1  1  2  2  2  4  2  2  2  2  1  1  2  2  1  1  1  1  1  1  1  1  4  1  1  1  1
 0 12  0 12  8  4  8  4  0 12  0 12  8  4  8  4  0 12  0 12  8  4  8  4  0 12  0 12  8 12  4 12  8  4  4  4  0  8  0 12  8  4  0 12 12 12  8  4  4  4  0  8 12  4  0  8 12  4  0  8 12  4  4  0  8  4  4  4 12  0  8 12  0  8  8  4  4  0  8 12  4  0  8  0  0  8  8 12 12  4  4  0  0  8  0  8
 0  0  8  8  8  8  0  0  0  0  8  8  8  8  0  0  0  0  8  8  8  8  0  0  0  0  8  8  8  0  0  8  0  8  8  0  8  8  0  0  0  0  8  8  8  0  8  8  8  0  8  8  0  8  0  0  8  0  0  0  0  8  0  8  8  8  0  0  8  8  8  0  0  0  0  8  0  8  8  8  8  0  0  0  8  8  0  0  8  8  0  0  0  0  8  8

generates a code of length 96 over Z16 who´s minimum homogenous weight is 96.

Homogenous weight enumerator: w(x)=1x^0+113x^96+10x^100+1x^104+2x^108+1x^120

The gray image is a code over GF(2) with n=768, k=7 and d=384.
This code was found by Heurico 1.16 in 0.968 seconds.