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  1  1  1  1  1  1  1  1  1  1  1  2  2  0  8  2  1  0  2  2  8  1  1  2  1  1 12  2  1  1  8  1  2  1  4  8  1  2  1  2  1  1  1  1 12  1  1  1  0  2  1  1  2  4  1  1  8  1  1  8  1  1  1 12  4  1  1
 0  2  0  0  0  2 14  2  4 12 14 10 12 14 12 14  4 12 14 10  4 10 14  4 14 10 10  0  8  0  2  2 12 10  6  8 12 10  6  8  0 14  8  8 14  4  4 10  2  2  4 12 12 10 10  0  4 12  4  2  6  8  0  4  8  8 10  2  8 14  6  8  8 12  4 10  0  2  2  2 14  8  0 14 10  2  4  2  4 12  0  8  2  2  2 14
 0  0  2  0  2  2 10  8  0  0  2 10  6  4 14  4  8  0  8 14  6 10  4 10 14  4 14 14  2  4  0 10  8  6  8  8  4  0 10 14  2 12 12  4  6 10  2 12  2  0  8  6  2  4  0  2  0  2  6  2  4  0 14  2  2  8  4  0 14  0 10  4 12  8 12  4 10  4 10 14 14 10  2  2 10 14  6  2  2  2  2  4  4  8 12  6
 0  0  0  2  2  8  2  6 14  4  4 14 14 10 12  4 10  8 12  2  2  4 14  8  8 14  6  6  4  4 12 10  2  4  6  0 14 14  4  4 14 14  2  2  4  2  0 14  6  8  2  4  0  0  8  2  6 10 10 14  6 14  4  6 12  6 14  8 10  0 14  0  6  2  4 12  6  6 12 14 10 10  0  0  6  2 14  4  2  2  2  0  4 12  6  0
 0  0  0  0  4  0  4 12 12 12 12  8  8  0 12 12 12  0  4  0  8  0  0  0 12  4  8  4 12  4  8 12  8  8  0  4  8  0  8 12  4  8  4  0  0  0  4  4 12 12  4  8 12 12  8 12  4  4  4  8 12  4  8 12  0  0  8 12  8  8  4  0  4  0 12  4  8 12  4 12 12  0  8  0  0  4  0 12  8  4  0 12  0 12  8  8

generates a code of length 96 over Z16 who´s minimum homogenous weight is 87.

Homogenous weight enumerator: w(x)=1x^0+266x^87+486x^88+758x^89+1028x^90+1366x^91+1892x^92+2406x^93+3144x^94+3284x^95+4063x^96+3314x^97+3137x^98+2228x^99+1733x^100+1146x^101+768x^102+598x^103+342x^104+306x^105+176x^106+134x^107+73x^108+52x^109+30x^110+12x^111+18x^112+2x^113+4x^114+1x^138

The gray image is a code over GF(2) with n=768, k=15 and d=348.
This code was found by Heurico 1.16 in 60 seconds.