The generator matrix

 1  0  0  1  1  1 10 14  1  1 12  1  1 10  1  1  6 12 10  1  1  1  0 14  1  1  1  2  8  1  1  0 12  1  1  1 12  1  1  1 10  1  1  0  1  1  1  4 10  4  1 14  0  1  1  4  2 10  1 14  1  1  1 12  1  1  8 14  1  8 10  1  1  1  1  1 12  1  2 10 10  8  1  1  1  1
 0  1  0  4  5  1  1  1  3 14  1 10  7  6  9 12  1 10  1 15  8  6  1  8  1  3 10  1  1  1  9  2  1  2  6  3  1 12  3  2  1  6  3  1  7  9  4  1  8  1  1  1  1  6  8  6  1  4 12  1  5  6  5 12  3  8  1  1 10  1  1  4  5  4  5 15  6  0  1 10 10  1  4  5 13  0
 0  0  1  7  3  4  3  2  3 15  5  0  4  1  6  5  0  1  9  5 14  5 11  1 13 10  6 12  2 10  3  1 15 11 10  9 12 14  0  1  7  4 15  9  2  0  8  8  1 14  7 11 12  5  6  1  2  1 11  8 14  0 13  1 15  3 15  5 14 14  5 14  0  5 11  6  1  8  3  1  1 14 15  6  3  0
 0  0  0  8  0  0  0  0  0  8  0  0  0  0  0  0  0  0  0  0  0  0  8  8  8  8  8  8  8  0  8  8  8  0  8  8  8  8  8  8  0  8  0  8  8  8  0  0  8  0  0  8  8  8  0  0  8  8  0  8  8  8  8  0  0  0  0  0  0  0  8  8  0  0  8  8  8  0  8  8  0  8  8  8  0  0
 0  0  0  0  8  0  8  8  0  8  0  8  0  8  8  8  0  8  0  8  8  0  0  8  8  0  0  8  0  8  0  0  0  8  0  0  0  8  8  8  8  8  0  8  8  0  8  8  0  8  0  8  8  0  0  0  8  0  0  0  8  0  0  8  8  8  0  8  0  8  0  8  8  0  8  0  8  8  0  0  8  0  0  8  0  0
 0  0  0  0  0  8  0  0  0  0  0  0  0  0  0  0  8  8  8  8  8  8  0  0  8  8  8  0  8  8  8  8  8  8  0  0  0  0  8  8  8  8  8  0  0  0  8  0  8  8  0  8  8  8  8  8  8  0  0  8  8  0  0  0  8  8  8  0  0  0  8  8  8  0  0  0  0  0  8  0  8  0  8  0  0  8

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

Homogenous weight enumerator: w(x)=1x^0+274x^79+524x^80+1996x^81+1773x^82+3598x^83+2660x^84+4620x^85+2680x^86+4516x^87+2524x^88+3400x^89+1402x^90+1286x^91+528x^92+576x^93+116x^94+156x^95+55x^96+28x^97+9x^98+20x^99+12x^100+4x^101+4x^102+6x^103

The gray image is a code over GF(2) with n=688, k=15 and d=316.
This code was found by Heurico 1.16 in 14.7 seconds.