The generator matrix

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

generates a code of length 57 over Z16 who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+256x^52+416x^53+890x^54+960x^55+1249x^56+992x^57+1198x^58+800x^59+668x^60+312x^61+232x^62+56x^63+88x^64+40x^65+14x^66+8x^67+8x^68+2x^70+1x^72+1x^80

The gray image is a code over GF(2) with n=456, k=13 and d=208.
This code was found by Heurico 1.16 in 1.02 seconds.