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

generates a code of length 57 over Z16 who´s minimum homogenous weight is 51.

Homogenous weight enumerator: w(x)=1x^0+184x^51+259x^52+532x^53+609x^54+948x^55+1156x^56+1138x^57+1023x^58+892x^59+489x^60+426x^61+199x^62+152x^63+65x^64+46x^65+25x^66+28x^67+12x^68+2x^69+4x^71+1x^72+1x^80

The gray image is a code over GF(2) with n=456, k=13 and d=204.
This code was found by Heurico 1.16 in 8.48 seconds.