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

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

Homogenous weight enumerator: w(x)=1x^0+90x^78+320x^79+579x^80+754x^81+1079x^82+1314x^83+1776x^84+1696x^85+1926x^86+1536x^87+1594x^88+950x^89+961x^90+614x^91+409x^92+282x^93+168x^94+108x^95+84x^96+72x^97+30x^98+28x^99+5x^100+6x^101+1x^102+1x^118

The gray image is a code over GF(2) with n=688, k=14 and d=312.
This code was found by Heurico 1.16 in 7.28 seconds.