The generator matrix

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

generates a code of length 86 over Z16 who´s minimum homogenous weight is 81.

Homogenous weight enumerator: w(x)=1x^0+148x^81+732x^82+1032x^83+1232x^84+936x^85+1084x^86+716x^87+621x^88+444x^89+456x^90+240x^91+245x^92+144x^93+88x^94+28x^95+18x^96+24x^97+2x^104+1x^108

The gray image is a code over GF(2) with n=688, k=13 and d=324.
This code was found by Heurico 1.16 in 1.28 seconds.