The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+72x^79+124x^80+386x^81+616x^82+1168x^83+1326x^84+1886x^85+1617x^86+2252x^87+1529x^88+1960x^89+1208x^90+1070x^91+528x^92+288x^93+151x^94+70x^95+30x^96+26x^97+18x^98+12x^99+11x^100+8x^101+6x^102+10x^103+2x^105+2x^107+2x^109+2x^112+2x^113+1x^116

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 5.48 seconds.