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

generates a code of length 86 over Z16 who´s minimum homogenous weight is 79.

Homogenous weight enumerator: w(x)=1x^0+56x^79+296x^80+360x^81+595x^82+728x^83+970x^84+846x^85+1034x^86+738x^87+765x^88+580x^89+428x^90+192x^91+226x^92+102x^93+89x^94+74x^95+44x^96+32x^97+21x^98+4x^99+10x^100+1x^126

The gray image is a code over GF(2) with n=688, k=13 and d=316.
This code was found by Heurico 1.16 in 1.89 seconds.