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

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

Homogenous weight enumerator: w(x)=1x^0+166x^78+48x^79+174x^80+704x^81+256x^82+240x^83+191x^84+32x^85+158x^86+49x^88+28x^90+1x^156

The gray image is a code over GF(2) with n=656, k=11 and d=312.
This code was found by Heurico 1.16 in 16.1 seconds.