The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+210x^79+793x^80+1522x^81+2343x^82+2734x^83+3806x^84+3366x^85+4137x^86+3380x^87+3299x^88+2450x^89+1992x^90+1162x^91+708x^92+434x^93+222x^94+58x^95+59x^96+32x^97+23x^98+6x^99+21x^100+1x^102+4x^105+2x^106+2x^107+1x^108

The gray image is a code over GF(2) with n=688, k=15 and d=316.
This code was found by Heurico 1.16 in 14.9 seconds.