The generator matrix

 1  0  1  1  1 14  1  2  1  8  1  1  4  1  1  1  1 12  1  1  1  1  0 12  6 10  6 10  0  1  1 12  1  1 14  1  1  6  1  1  0 14 14  0  8  4 12  1  1  1  1  0  1  1  1  1
 0  1 11  6 13  1 12  1  7  1 10  1  1  8  3 14  5  1  4 15  2  9  1  1  1  1  1  1  1  0 11  1 10 13  1 12  1  1  6  7  2  1  1  1  2  1  1 15  5 14  2  1  7  5 12  8
 0  0 12  0  4  4  8  4  4 12  8 12 12  4  0 12  8  8  4  0 12  8  0  8  0  0  0  0 12  0 12 12  8  4 12  0  4 12  8 12  4  8  8  8  0  0  0  8  8  4 12 12  0  4  0  4
 0  0  0  8  0  8  8  8  8  0  0  8  0  0  0  0  0  0  8  8  8  8  8  8  0  8  0  8  8  8  8  8  8  8  0  0  0  0  0  0  0  8  0  0  0  0  8  0  8  8  0  0  0  8  8  0
 0  0  0  0  8  8  8  0  8  8  8  0  0  0  8  8  0  8  0  8  8  0  0  8  0  8  8  0  8  0  0  0  8  8  8  8  0  0  0  8  0  8  0  8  8  8  0  0  8  0  0  0  8  0  0  8

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

Homogenous weight enumerator: w(x)=1x^0+393x^52+240x^53+632x^54+400x^55+845x^56+400x^57+600x^58+240x^59+267x^60+48x^62+16x^64+6x^68+6x^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 50.4 seconds.