The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  1  4  1  2  1  1  2  1  1  2  1  1  1  1  1  1  1  8  1  4  1  1  4  2  1  1  2  1  1  1  1  2  1  1  0  1  1  1  2 12  0  1  4  1  2  1  1  8  2  4  8  1
 0  2  0  2  0  0  6 14  4  4 10  6 12  6 10  4  4 12  2  2  4  8  6  0 10 12  6  2 14  0  8  2  4 10  2 12  6  4 12  4  6 10  6 14 12  6  8 14  8 14  4  2  8  2  8  6  2  8  8  6 14  0 12  0  0  2 10  4  2 14  4  8  0  2  2 12  4 14  2  8  8  2  0  2  2 12
 0  0  2  2 12  6  6  4  4  2  6  0  8 10  4 14  4 10  6 10  6  0  0 14  0  8  4 10 10  2 12  4  4 14 12  2  2  2  6  2  8  4 14 12 12  8 10  6 14  8  2  2  8 12 14  2 10  2 10 12  4 12  8  4  8  2 14  6  6  8 12  0  6  6  8  8  2  6 14  0  6  0 10 10  2  6
 0  0  0  8  0  0  8  0  0  0  8  8  8  0  8  8  8  0  0  0  8  0  0  8  8  8  0  8  0  8  8  8  8  8  0  0  8  0  0  8  0  0  0  0  0  8  0  8  0  0  8  0  8  0  8  8  0  8  0  8  8  0  0  8  0  8  8  0  0  8  8  8  0  8  0  0  8  8  8  8  0  0  0  8  8  8
 0  0  0  0  8  0  8  0  8  8  0  0  0  8  0  0  8  8  0  0  0  0  8  8  8  8  8  8  8  8  0  8  8  8  0  8  0  8  0  0  0  0  0  8  0  0  8  0  0  8  8  8  0  0  8  8  8  8  8  8  8  8  8  8  8  8  8  8  0  8  0  0  0  0  0  0  8  0  0  8  8  8  0  0  8  8
 0  0  0  0  0  8  0  8  8  0  8  0  0  8  8  8  0  8  8  0  0  8  0  8  8  8  8  8  0  0  8  0  8  8  8  0  8  8  8  8  8  0  8  8  8  8  8  0  0  8  8  8  0  0  0  0  0  8  0  0  8  8  0  0  8  0  8  8  8  8  8  8  8  8  8  0  8  8  8  0  0  0  0  0  8  0

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

Homogenous weight enumerator: w(x)=1x^0+120x^79+219x^80+482x^81+394x^82+766x^83+703x^84+1108x^85+1118x^86+940x^87+610x^88+506x^89+301x^90+420x^91+105x^92+184x^93+69x^94+54x^95+21x^96+24x^97+36x^98+2x^99+4x^100+1x^102+2x^103+1x^104+1x^130

The gray image is a code over GF(2) with n=688, k=13 and d=316.
This code was found by Heurico 1.16 in 2.24 seconds.