The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+44x^78+186x^79+345x^80+760x^81+1058x^82+1416x^83+1705x^84+1708x^85+1987x^86+1832x^87+1660x^88+1452x^89+1002x^90+654x^91+287x^92+120x^93+48x^94+24x^95+20x^96+14x^97+15x^98+12x^99+11x^100+8x^101+5x^102+2x^103+2x^104+2x^105+2x^107+1x^114+1x^124

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 5.43 seconds.