The generator matrix

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

generates a code of length 56 over Z16 who´s minimum homogenous weight is 51.

Homogenous weight enumerator: w(x)=1x^0+220x^51+435x^52+770x^53+1144x^54+1196x^55+1065x^56+1032x^57+998x^58+594x^59+320x^60+208x^61+93x^62+44x^63+22x^64+20x^65+12x^66+10x^67+4x^68+2x^69+1x^70+1x^76

The gray image is a code over GF(2) with n=448, k=13 and d=204.
This code was found by Heurico 1.16 in 10.4 seconds.