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

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

Homogenous weight enumerator: w(x)=1x^0+229x^52+32x^53+224x^54+352x^55+383x^56+352x^57+224x^58+32x^59+208x^60+7x^64+3x^68+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 0.306 seconds.