The generator matrix

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

generates a code of length 86 over Z16 who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+511x^78+1722x^79+3651x^80+6020x^81+8023x^82+10226x^83+12904x^84+14736x^85+15352x^86+15458x^87+12982x^88+10662x^89+7782x^90+4890x^91+3144x^92+1648x^93+747x^94+324x^95+112x^96+84x^97+43x^98+20x^99+20x^100+6x^102+2x^104+2x^105

The gray image is a code over GF(2) with n=688, k=17 and d=312.
This code was found by Heurico 1.16 in 198 seconds.