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

generates a code of length 85 over Z16 who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+129x^78+218x^79+448x^80+456x^81+872x^82+602x^83+1273x^84+628x^85+1154x^86+610x^87+656x^88+304x^89+258x^90+130x^91+208x^92+76x^93+72x^94+36x^95+35x^96+8x^97+10x^98+4x^99+3x^100+1x^126

The gray image is a code over GF(2) with n=680, k=13 and d=312.
This code was found by Heurico 1.16 in 2.19 seconds.