The generator matrix

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

generates a code of length 86 over Z16 who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+114x^80+316x^81+769x^82+752x^83+993x^84+868x^85+1104x^86+690x^87+780x^88+606x^89+572x^90+248x^91+185x^92+36x^93+50x^94+34x^95+20x^96+26x^97+15x^98+4x^99+2x^100+4x^101+1x^102+1x^104+1x^118

The gray image is a code over GF(2) with n=688, k=13 and d=320.
This code was found by Heurico 1.16 in 1.73 seconds.