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

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

Homogenous weight enumerator: w(x)=1x^0+256x^52+32x^53+80x^54+352x^55+613x^56+352x^57+80x^58+32x^59+240x^60+9x^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 0.437 seconds.