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

generates a code of length 82 over Z16 who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+495x^76+40x^77+752x^78+328x^79+1406x^80+680x^81+1260x^82+640x^83+1092x^84+296x^85+484x^86+56x^87+418x^88+8x^89+116x^90+93x^92+12x^94+14x^96+1x^128

The gray image is a code over GF(2) with n=656, k=13 and d=304.
This code was found by Heurico 1.16 in 22.7 seconds.