The generator matrix

 1  0  1  1  1  6  1  1  8  1  1 14  4  2  1  1  1  1 10  1  1  1 12  1  0  1  1  1  1  1  1  6  2  1  1 12  1 10  1  1  4  1  1  1 14  1  1  1  1  0  1 14  1  1  1  1  1  1 14  8  4  6  1 12  1  1  1  6  1  1 12  1  1  1  1 14  1  1  1  1  6  1  1  1  1  1  0  1 14  1  4  8  2  0  0  1
 0  1 11  6 13  1 12  7  1 10  1  1  1  1  3 14  5  8  1  4  9 15  1  2  1  5  2 11  0 13 12  1  1  7  6  1 10  1  8 11  1  9 10  8  1 13 11 11 10  1  1  1  8  7  4  3 14 12  1  1  1  1  1  1  5 13  5  1 11 10  1  8  6  9 15  1  9 12  0 10  1  9 10 13  9 11  1  0  1  8  0  8  8  1  1  8
 0  0 12  0  4  0  0  4  4  8  4 12 12 12  0 12  0 12  8 12  8  8  0 12  0  0 12  4  0 12  8  0  4 12  8  8  8  0 12 12 12  0  8 12 12  4  0  4  4  8 12 12 12 12 12  8 12  8 12  4 12  8 12  0  4  4  0  4  0  8 12  0 12  8  8  8  8  8  4 12  8  4  8  8  8  8  8  8 12  4  4  4  4  0  8  4
 0  0  0  8  0  0  0  0  0  8  8  8  8  0  8  0  0  8  8  0  8  0  0  8  0  8  8  8  8  8  0  0  8  0  8  8  8  8  8  0  8  8  0  8  0  0  0  8  8  0  8  0  8  0  0  0  8  8  0  0  0  8  0  0  0  8  8  8  0  0  0  0  8  0  0  0  8  8  0  8  0  0  0  0  8  8  0  0  8  8  0  8  0  0  8  0
 0  0  0  0  8  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  8  8  8  8  8  8  8  0  8  8  8  8  0  8  8  0  8  0  8  0  8  0  8  0  8  0  0  0  0  8  8  8  8  8  8  8  0  8  0  8  8  8  0  0  0  0  8  0  8  0  0  0  0  8  0  8  0  8  0  8  0  8  0  8  8  0  8  0  8  0  0  0  8  0  8
 0  0  0  0  0  8  0  0  0  0  0  0  0  0  8  8  8  8  8  8  8  8  8  8  8  8  8  0  0  0  0  0  8  8  8  0  8  0  0  8  8  0  8  0  8  0  0  8  0  0  0  8  0  8  0  0  8  8  8  8  0  8  0  0  0  8  0  0  8  8  0  8  0  0  0  8  8  8  0  8  8  0  0  0  0  0  8  8  8  0  8  0  8  8  0  0
 0  0  0  0  0  0  8  0  0  8  0  0  8  8  8  0  0  8  0  8  8  8  8  0  8  0  8  0  0  8  0  0  8  0  0  0  0  0  8  0  8  8  8  8  0  0  8  0  0  0  8  8  0  8  8  8  8  8  0  8  8  0  8  8  8  0  0  0  8  0  0  0  8  0  0  8  8  0  8  0  0  0  8  0  8  0  0  8  8  8  8  0  8  0  8  0
 0  0  0  0  0  0  0  8  8  0  8  8  0  0  0  0  8  8  0  0  8  8  0  0  8  0  0  8  8  8  8  8  8  8  0  0  8  8  8  0  8  0  8  0  0  8  8  0  0  8  0  0  8  8  0  0  8  0  8  0  0  8  8  0  0  8  0  0  8  0  0  0  8  8  8  8  8  0  8  8  0  0  0  0  8  0  8  8  8  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+52x^86+152x^87+263x^88+520x^89+839x^90+1470x^91+1679x^92+2968x^93+2791x^94+4130x^95+3258x^96+4206x^97+2700x^98+2902x^99+1672x^100+1406x^101+700x^102+502x^103+234x^104+94x^105+62x^106+36x^107+38x^108+14x^109+14x^110+24x^111+17x^112+4x^113+6x^114+2x^116+4x^117+2x^118+3x^120+1x^122+1x^124+1x^126

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 24.3 seconds.