The generator matrix

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

generates a code of length 86 over Z16 who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+499x^80+448x^81+1508x^82+1416x^83+1925x^84+1736x^85+1864x^86+1808x^87+1656x^88+1232x^89+1080x^90+488x^91+377x^92+40x^93+124x^94+115x^96+28x^98+32x^100+4x^102+1x^108+1x^112+1x^116

The gray image is a code over GF(2) with n=688, k=14 and d=320.
This code was found by Heurico 1.16 in 86.9 seconds.