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

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

Homogenous weight enumerator: w(x)=1x^0+25x^86+4x^87+143x^88+96x^89+328x^90+180x^91+546x^92+428x^93+953x^94+812x^95+1211x^96+860x^97+928x^98+444x^99+519x^100+132x^101+278x^102+96x^103+109x^104+20x^105+34x^106+20x^108+6x^110+6x^112+4x^114+3x^116+1x^118+1x^120+2x^122+1x^126+1x^152

The gray image is a code over GF(2) with n=768, k=13 and d=344.
This code was found by Heurico 1.16 in 3.14 seconds.