The generator matrix

 1  0  0  1  1  1 10  2  1  1  1  1 14 12  1  1 12  0  1  1  8  1  1  6 10  6  1  1  1 10  4 14  6  1  2  1  1  4  1  1  4  8  1  8  0  0  1 10  1  1  1 10  1  1  2 12  1
 0  1  0  0  5 13  1  6  1  9  4  4  1  1 14  3  1 10 10 15  1 15 14  1  1  4  6  5  3  1  1  2  0  1  1  6  6  1  7 10 14 10  7  4  1  1 12  1  1  1  5  4 10  5  6  0  1
 0  0  1 11  7  4  7  1  1  2  6 13  6  5  5  1 15  1  6 12 14 14  4 12  1  1 15  1  7 11 14  1  1  7  2 10 15 15  7  7  1  1 14  1 12  5  5 13  8  5  1  1  6 15  1  1 11
 0  0  0 12 12  0 12  4  0 12  4  8  4  0 12 12  4  8  0  4  0  8  4  0 12 12 12  8  4  0 12  8  8  0  0  8  0  8 12  8  0 12  4  4  4  0  0  4  8 12  4  4  4  4  8  4 12

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

Homogenous weight enumerator: w(x)=1x^0+426x^52+952x^53+1580x^54+2116x^55+2331x^56+2188x^57+2262x^58+1652x^59+1301x^60+764x^61+428x^62+228x^63+81x^64+28x^65+30x^66+4x^67+4x^69+4x^70+3x^72+1x^76

The gray image is a code over GF(2) with n=456, k=14 and d=208.
This code was found by Heurico 1.16 in 2.3 seconds.