The generator matrix

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

generates a code of length 82 over Z16 who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+508x^78+352x^79+660x^80+324x^81+662x^82+268x^83+544x^84+284x^85+289x^86+52x^87+96x^88+24x^90+4x^92+21x^94+4x^96+1x^100+1x^108+1x^112

The gray image is a code over GF(2) with n=656, k=12 and d=312.
This code was found by Heurico 1.16 in 3.65 seconds.