The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+189x^78+806x^79+1525x^80+2386x^81+2848x^82+3526x^83+3505x^84+4104x^85+3252x^86+3334x^87+2566x^88+1970x^89+1194x^90+760x^91+398x^92+200x^93+93x^94+48x^95+36x^96+8x^97+4x^98+6x^99+1x^100+4x^101+2x^102+2x^106

The gray image is a code over GF(2) with n=680, k=15 and d=312.
This code was found by Heurico 1.16 in 14.7 seconds.