The generator matrix

 1  0  1  1  1  6  1  1 12  1 10  1  1  1  0  1  1  6  1  1 12  1  1 10  1 10  1  0  1  1  1  1  1 12  1  6  1  1  6  1  1  1  0  1  1  1  1  1  1  1  1 12  1  1  6  1  1  0  1 10  0 10  8  1  1 10 12  1  1  0  1  1  6  6  1  1  1  1  1  1  1  1  1  8  8  1  4 12  1  1  2  1  1  1  1  1
 0  1  3  6  5  1 12  7  1 10  1  9  0  3  1  6  5  1 12 15  1 10  9  1  0  1  3  1  5  6 15  9 10  1 12  1  4  3  1  0  5  6  1  9  3 10 15  1 12  5  6  1  6  0  1  9  7  1  3  1  1  1  1  6 12  1  1 12 10  1  0  9  1  1 15  3  5  1  9 11 10 10 15  1  1 15  2  2 14 11  1 14  2  6 14  0
 0  0  8  0  0  0  0  0  0  0  0  0  0  0  8  0  8  8  0  0  0  0  8  0  0  0  8  8  8  8  8  8  8  8  8  8  8  0  8  8  0  8  8  0  0  8  8  8  0  0  8  8  8  0  0  8  0  0  8  0  8  8  8  8  8  0  0  8  0  0  0  8  8  0  0  8  8  8  8  0  0  0  0  8  0  8  8  0  8  8  8  0  8  8  0  0
 0  0  0  8  0  0  0  0  0  0  0  8  8  8  0  0  0  0  0  0  0  8  8  8  8  8  8  8  8  8  8  8  0  8  0  0  0  8  0  0  8  0  8  0  8  8  0  0  0  8  8  0  8  0  8  0  8  8  8  0  8  0  8  8  8  0  0  0  0  8  0  8  0  8  0  8  8  0  0  0  0  8  8  8  8  0  0  0  8  0  8  8  0  0  8  0
 0  0  0  0  8  0  0  0  0  0  0  0  8  8  0  8  0  0  8  8  8  0  8  0  0  0  8  8  0  0  8  8  0  8  8  8  0  8  8  8  8  8  0  8  8  8  0  0  8  0  0  0  0  0  8  8  0  8  8  8  8  8  0  8  0  0  0  8  0  8  0  0  8  8  0  0  0  0  0  0  8  8  0  8  8  8  8  8  8  8  8  0  8  0  0  8
 0  0  0  0  0  8  0  0  8  0  8  8  8  0  0  8  8  8  0  8  8  8  8  0  8  0  0  8  8  0  0  0  0  8  0  0  0  8  8  8  8  8  0  0  0  0  8  0  8  8  0  8  8  8  0  8  0  8  8  0  0  0  8  8  8  0  0  0  0  8  8  0  0  0  8  8  8  8  0  0  0  0  8  0  8  8  0  0  0  8  8  8  8  8  8  8
 0  0  0  0  0  0  8  0  8  8  8  0  0  0  0  0  0  0  8  8  8  0  8  8  8  0  8  8  8  8  8  0  0  0  8  0  8  8  0  8  0  0  0  0  8  8  8  8  0  8  0  8  0  0  8  8  8  0  8  0  0  8  8  0  8  0  8  0  0  8  0  0  0  0  8  0  0  8  8  8  0  8  8  8  0  0  8  0  0  8  0  8  0  0  8  0
 0  0  0  0  0  0  0  8  8  8  0  8  0  8  8  8  8  0  0  8  0  0  8  0  0  0  0  0  0  8  8  8  8  8  0  0  0  0  0  8  8  0  0  8  8  8  8  8  0  0  0  8  0  8  0  8  8  8  0  0  0  8  0  0  0  8  8  8  8  0  0  0  8  0  8  8  0  0  0  8  0  0  0  8  0  8  8  8  8  0  0  8  8  0  0  8

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

Homogenous weight enumerator: w(x)=1x^0+48x^87+96x^88+276x^89+323x^90+954x^91+648x^92+1614x^93+1087x^94+2532x^95+1362x^96+2456x^97+1093x^98+1560x^99+645x^100+988x^101+278x^102+268x^103+49x^104+36x^105+20x^106+14x^107+9x^108+6x^109+2x^110+3x^112+8x^114+1x^116+1x^120+3x^122+1x^124+1x^126+1x^130

The gray image is a code over GF(2) with n=768, k=14 and d=348.
This code was found by Heurico 1.16 in 58.2 seconds.