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

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

Homogenous weight enumerator: w(x)=1x^0+135x^52+64x^53+338x^54+360x^55+442x^56+284x^57+208x^58+28x^59+85x^60+20x^61+46x^62+12x^63+24x^64+1x^104

The gray image is a code over GF(2) with n=448, k=11 and d=208.
This code was found by Heurico 1.16 in 2.05 seconds.