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

generates a code of length 86 over Z16 who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+62x^78+136x^79+210x^80+372x^81+386x^82+636x^83+892x^84+936x^85+1091x^86+978x^87+836x^88+590x^89+338x^90+284x^91+171x^92+90x^93+63x^94+22x^95+23x^96+32x^97+9x^98+6x^99+2x^100+10x^101+2x^102+8x^104+2x^105+2x^107+1x^114+1x^132

The gray image is a code over GF(2) with n=688, k=13 and d=312.
This code was found by Heurico 1.16 in 2.4 seconds.