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

generates a code of length 87 over Z16 who´s minimum homogenous weight is 79.

Homogenous weight enumerator: w(x)=1x^0+188x^79+314x^80+512x^81+761x^82+978x^83+1338x^84+1698x^85+1845x^86+1778x^87+1794x^88+1416x^89+1087x^90+862x^91+589x^92+428x^93+259x^94+234x^95+115x^96+42x^97+63x^98+32x^99+7x^100+14x^101+13x^102+8x^103+2x^104+2x^105+3x^106+1x^118

The gray image is a code over GF(2) with n=696, k=14 and d=316.
This code was found by Heurico 1.16 in 30.7 seconds.