The generator matrix

 1  0  1  1  1  6  1  1  8  1  1 14  1 12  1  1  1 10  4  1  1  2  1  1  1 10  1  0  1  1  1  1  1  1 12 10  0  1  1  1  2  1 12 12  1  1 14  1  1 10  0  1  2  8  1  1
 0  1 11 14 13  1  2  3  1 12  5  1  7  1  8  9  6  1  1  4 15  1 10  1 13  1  7  1  0 10 12  6 11  1  1  1  1 11  0 12 10  7  1  2 13  6  1 10  9  1  2  0  8  4  8  8
 0  0 12  4 12  8  4  0  4  8  8 12  4  8 12  8  8  8  4 12  0 12  0 12  4  0  4  0  0  0  8  8 12  4  8  0  4  0 12 12  8  0  4  0  8  4 12  4  8 12  0  8  0 12  4 12
 0  0  0  8  8  8  0  8  8  8  0  0  8  8  8  8  0  0  0  0  0  8  8  0  8  0  0  8  8  0  0  8  8  0  0  8  0  0  0  8  8  8  8  8  8  0  8  8  0  0  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+78x^52+264x^53+330x^54+252x^55+234x^56+292x^57+296x^58+164x^59+68x^60+52x^61+12x^62+1x^64+2x^70+2x^84

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 0.158 seconds.