The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+662x^79+1876x^80+3298x^81+4204x^82+5506x^83+6341x^84+7662x^85+7073x^86+7556x^87+6610x^88+5442x^89+3741x^90+2544x^91+1435x^92+830x^93+339x^94+218x^95+84x^96+44x^97+35x^98+18x^99+4x^100+4x^101+4x^103+1x^104+4x^107

The gray image is a code over GF(2) with n=688, k=16 and d=316.
This code was found by Heurico 1.16 in 56.8 seconds.