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

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

Homogenous weight enumerator: w(x)=1x^0+168x^78+332x^79+585x^80+644x^81+1084x^82+1180x^83+1647x^84+1768x^85+1990x^86+1720x^87+1561x^88+1104x^89+930x^90+548x^91+390x^92+248x^93+176x^94+84x^95+106x^96+44x^97+30x^98+8x^99+23x^100+6x^102+6x^104+1x^120

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 7.96 seconds.