The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+164x^78+644x^79+810x^80+532x^81+486x^82+420x^83+271x^84+228x^85+138x^86+124x^87+105x^88+80x^89+60x^90+20x^91+10x^92+2x^96+1x^108

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 0.438 seconds.