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  1  1  1  2  1  2  2  2  1  2  1  1  1  1  1  1  2  1  4  1  1  4  1  1  2  1  1  2  1  1  4  1  2  1  4  1  1  4  2  4  1  1  1  2  1  0  1  0  0  1  1  1  2  1  4  1  4  1  1  1
 0 12  0  0  0  4 12  4  0  8  4 12  0  8 12  0  4  4  8  4 12 12  8  8 12  0  4  8  0  4  0 12  4  4  0  0  4 12  0  4  8  0  0  8 12  0  0  4  4  0  8  0  4  4  0  4  4 12  4  8  0  8  0  8 12  4 12  4  4  0  4  4  4  8  8 12  8 12  4  4  0  4  8  8  0  4 12  8  4  8  8  8  8  4  4  0
 0  0 12  0  4  4 12  0  0  0  4  8  4  4  0  8  4  4 12  8 12  0  8  4  8  8  8  8  4  4 12 12 12 12 12  4  0  0  8  0  4 12  4 12  0  8  0  4  0  4  4  4 12  4 12  4  0  8  0 12 12 12  8  4  8  4  8 12  8  8  0 12 12 12  4  4  0  8  0  4  0  4  4  8  4  8  0  0 12 12  4  8 12  0 12  0
 0  0  0 12  4  0 12  4  0  4 12  8 12  0  4  8  8  8  4  0  4  4 12  0  0  4  0  0  8 12  4  4  8  8 12 12  0  4  0 12 12  8 12 12  8  4  0  0 12  8  0  0  8  4  0 12  0  0  8  8  0  4 12  0  4  4  8  4  4 12 12 12 12  4  8  4  0  4  0 12 12  4  0  4  8 12  0 12  0  4  8 12  4  8  4  0
 0  0  0  0  8  0  0  0  8  0  8  8  0  0  0  0  8  8  8  0  8  8  0  8  8  8  8  8  0  8  8  8  0  0  0  0  8  0  0  0  8  8  8  8  8  8  0  8  8  8  0  0  0  8  0  0  0  0  0  8  0  0  8  8  0  0  8  0  0  0  8  8  0  0  8  0  0  8  0  0  8  0  0  8  0  8  0  8  8  0  0  0  0  8  8  0
 0  0  0  0  0  8  0  0  8  8  8  0  8  0  8  8  0  8  8  0  8  8  0  8  0  8  0  8  0  0  0  0  0  8  0  8  8  0  0  8  0  8  8  0  8  8  8  0  0  8  8  8  0  8  0  8  0  0  8  0  8  8  0  0  8  0  8  0  8  8  0  8  8  0  0  8  0  0  8  8  0  8  0  8  8  0  8  0  8  0  8  0  0  0  0  0
 0  0  0  0  0  0  8  0  0  0  0  0  0  8  8  8  0  0  8  8  8  8  0  0  0  0  8  8  8  0  8  0  8  8  8  8  0  0  8  0  8  0  8  0  8  8  8  8  0  8  0  8  0  8  8  8  8  0  8  8  8  0  8  8  0  8  8  0  8  8  8  0  0  0  0  8  8  0  0  0  0  8  0  0  8  0  0  8  8  8  8  8  8  8  0  0
 0  0  0  0  0  0  0  8  8  8  0  8  0  0  0  0  0  8  0  8  8  0  8  8  0  8  0  8  8  8  0  0  8  8  0  0  8  0  0  0  8  0  8  0  8  0  8  8  0  8  0  8  8  0  8  8  0  8  0  0  0  8  8  0  8  8  8  8  8  0  0  0  0  0  8  8  8  8  8  8  8  0  8  8  8  0  0  0  0  0  0  8  8  8  0  0

generates a code of length 96 over Z16 who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+37x^84+86x^85+139x^86+130x^87+184x^88+400x^89+274x^90+718x^91+566x^92+1522x^93+1173x^94+2262x^95+1516x^96+2464x^97+1150x^98+1434x^99+528x^100+660x^101+200x^102+232x^103+154x^104+170x^105+93x^106+60x^107+56x^108+60x^109+31x^110+24x^111+24x^112+14x^113+9x^114+4x^115+5x^116+1x^118+1x^122+1x^128+1x^146

The gray image is a code over GF(2) with n=768, k=14 and d=336.
This code was found by Heurico 1.16 in 13.3 seconds.