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

generates a code of length 96 over Z16 who´s minimum homogenous weight is 86.

Homogenous weight enumerator: w(x)=1x^0+87x^86+110x^87+280x^88+280x^89+483x^90+590x^91+822x^92+1366x^93+1287x^94+2306x^95+1386x^96+2270x^97+1197x^98+1352x^99+830x^100+586x^101+414x^102+214x^103+210x^104+80x^105+91x^106+26x^107+40x^108+14x^109+17x^110+10x^111+9x^112+10x^113+4x^114+4x^116+2x^117+3x^118+2x^120+1x^146

The gray image is a code over GF(2) with n=768, k=14 and d=344.
This code was found by Heurico 1.16 in 10.9 seconds.