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

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

Homogenous weight enumerator: w(x)=1x^0+157x^78+312x^79+606x^80+628x^81+1177x^82+1284x^83+1601x^84+1664x^85+1973x^86+1736x^87+1469x^88+1156x^89+903x^90+516x^91+423x^92+232x^93+212x^94+120x^95+106x^96+32x^97+46x^98+13x^100+10x^102+2x^104+2x^106+2x^108+1x^116

The gray image is a code over GF(2) with n=688, k=14 and d=312.
This code was found by Heurico 1.16 in 8.15 seconds.