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

generates a code of length 87 over Z16 who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+66x^80+344x^81+414x^82+602x^83+652x^84+872x^85+877x^86+952x^87+803x^88+730x^89+570x^90+470x^91+262x^92+224x^93+110x^94+68x^95+54x^96+58x^97+28x^98+20x^99+1x^100+12x^101+1x^102+1x^124

The gray image is a code over GF(2) with n=696, k=13 and d=320.
This code was found by Heurico 1.16 in 1.9 seconds.