The generator matrix

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

generates a code of length 56 over Z16 who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+393x^52+1000x^53+1138x^54+1440x^55+1230x^56+940x^57+636x^58+480x^59+427x^60+256x^61+122x^62+96x^63+12x^64+12x^65+8x^66+1x^72

The gray image is a code over GF(2) with n=448, k=13 and d=208.
This code was found by Heurico 1.16 in 0.63 seconds.