The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+88x^80+416x^81+692x^82+762x^83+993x^84+892x^85+899x^86+734x^87+974x^88+592x^89+505x^90+306x^91+159x^92+60x^93+20x^94+50x^95+4x^96+16x^97+10x^98+4x^99+4x^100+8x^101+1x^104+1x^110+1x^114

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 1.7 seconds.