The generator matrix

 1  0  1  1  4  1 10  1  1  1  1  6 10  1  1  1  1  4  1  1 10  1  1  8  4 14  2  0  1  1  1  1  1  1  1  1 10  0 12  1  1  1  2  1  0  1  1  1  4  1  1  1  1  1  1  1
 0  1  1  6  1  7  1  4 15  2  5  1  1  8  3 14 13  1 10  9  1  0 15  1  1  1  1  1 14  2  2 12  0 14 12 12  1  1  1  3  1  9  1 11  1  7  1  7  1 10  5  5 14 10  8  5
 0  0  2  0 10  2  6 10  8 10  8  0 10 14  6 14  6  6  0  8  0  0  8  4 12  4  4  0 12 12 14 10  6  2 12 12 14  6 10 10 12  6  2  4 14 12  6 14  8  8 12  4  2  4 12 14
 0  0  0  8  0  8  8  8  8  0  0  8  8  8  8  0  0  0  0  8  0  8  0  8  0  8  0  8  0  8  8  0  0  8  0  8  0  8  8  0  8  8  0  0  8  8  0  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+191x^52+576x^53+556x^54+548x^55+470x^56+544x^57+520x^58+440x^59+143x^60+32x^61+20x^62+36x^63+8x^64+8x^66+1x^72+2x^76

The gray image is a code over GF(2) with n=448, k=12 and d=208.
This code was found by Heurico 1.16 in 0.318 seconds.