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

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

Homogenous weight enumerator: w(x)=1x^0+201x^86+212x^87+494x^88+552x^89+975x^90+1532x^91+1609x^92+2688x^93+2610x^94+4240x^95+2962x^96+4408x^97+2343x^98+2588x^99+1563x^100+1348x^101+792x^102+584x^103+373x^104+204x^105+187x^106+56x^107+137x^108+12x^109+52x^110+4x^111+25x^112+4x^113+7x^114+3x^116+1x^118+1x^136

The gray image is a code over GF(2) with n=768, k=15 and d=344.
This code was found by Heurico 1.16 in 35.5 seconds.