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

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

Homogenous weight enumerator: w(x)=1x^0+35x^84+20x^85+75x^86+70x^87+87x^88+104x^89+111x^90+234x^91+234x^92+732x^93+614x^94+1388x^95+859x^96+1404x^97+579x^98+752x^99+204x^100+248x^101+72x^102+90x^103+62x^104+44x^105+55x^106+22x^107+30x^108+8x^109+22x^110+4x^111+12x^112+5x^114+5x^116+1x^118+3x^120+1x^122+4x^124+1x^154

The gray image is a code over GF(2) with n=768, k=13 and d=336.
This code was found by Heurico 1.16 in 3.98 seconds.