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

generates a code of length 96 over Z16 who´s minimum homogenous weight is 88.

Homogenous weight enumerator: w(x)=1x^0+44x^88+72x^89+88x^90+88x^91+147x^92+186x^93+408x^94+742x^95+724x^96+682x^97+436x^98+132x^99+77x^100+50x^101+41x^102+38x^103+39x^104+24x^105+8x^106+16x^107+12x^108+8x^109+10x^110+8x^111+8x^112+2x^113+4x^116+1x^166

The gray image is a code over GF(2) with n=768, k=12 and d=352.
This code was found by Heurico 1.16 in 1.34 seconds.