The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+102x^79+379x^80+778x^81+1232x^82+1466x^83+1628x^84+1738x^85+2113x^86+1742x^87+1730x^88+1266x^89+845x^90+526x^91+360x^92+212x^93+87x^94+60x^95+41x^96+34x^97+25x^98+8x^99+2x^100+2x^101+2x^105+2x^106+2x^108+1x^112

The gray image is a code over GF(2) with n=688, k=14 and d=316.
This code was found by Heurico 1.16 in 5.35 seconds.