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  2  1  2  1  2  1  2  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  2  2  2  2  4  0  2  2  4  4  4  2  8  2
 0 12  0  4  0  0  4 12  0  0  4 12  0  0  4 12  0  0  4 12  0  0  4 12  0  4  0  8 12  8  0  8  4  8  0 12  8 12  8  4  8 12  8  4  8 12  8  4  8 12  8  4  8 12  8  4  8  8 12  4  8  8 12  4  8  8 12  4  4  4 12  4  8  0 12 12  8 12 12  0  0  0
 0  0 12  4  0 12  4  0  0 12  4  0  0 12  4  0  8  4 12  8  8  4 12  8  8 12  4  4  8  4  8  4 12  4  4  8  8 12  4  8  8 12  4  8  8  4  4  0  8  4  4  0  0 12 12  8  0 12  4  0  0 12  4  8  0 12 12  0  4 12  0  0  4  4  0  8  8  0  8 12  4  0
 0  0  0  8  0  0  8  0  8  8  0  8  8  8  0  8  8  8  8  8  8  8  8  8  0  0  0  0  0  0  0  8  0  8  0  0  0  0  0  0  0  0  0  0  8  8  8  8  8  8  8  8  8  8  8  8  0  0  0  0  8  8  0  8  0  0  8  0  0  8  0  8  0  8  0  8  0  8  8  0  8  0
 0  0  0  0  8  8  8  8  8  8  0  8  0  0  8  0  0  0  0  0  8  8  8  8  8  8  8  0  8  8  0  8  0  0  0  0  0  0  0  0  8  8  8  8  8  0  8  0  0  8  0  8  0  8  0  8  8  0  8  0  8  8  0  0  0  8  0  8  0  0  0  0  8  8  8  0  8  8  0  8  0  0

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

Homogenous weight enumerator: w(x)=1x^0+68x^78+16x^79+240x^80+112x^81+184x^82+112x^83+198x^84+16x^85+36x^86+38x^88+2x^92+1x^128

The gray image is a code over GF(2) with n=656, k=10 and d=312.
This code was found by Heurico 1.16 in 0.512 seconds.