The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+92x^79+418x^80+898x^81+1536x^82+1886x^83+2887x^84+3238x^85+4025x^86+3898x^87+3411x^88+3050x^89+2606x^90+1888x^91+1365x^92+608x^93+422x^94+202x^95+141x^96+72x^97+33x^98+30x^99+28x^100+6x^101+16x^102+4x^103+4x^104+1x^106+1x^110+1x^112

The gray image is a code over GF(2) with n=696, k=15 and d=316.
This code was found by Heurico 1.16 in 18.5 seconds.