The generator matrix

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

generates a code of length 64 over Z16 who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+293x^56+492x^57+1270x^58+1952x^59+3375x^60+5068x^61+6942x^62+9032x^63+9102x^64+8712x^65+6896x^66+5184x^67+3466x^68+1712x^69+1018x^70+504x^71+272x^72+76x^73+86x^74+32x^75+30x^76+4x^77+12x^78+4x^80+1x^84

The gray image is a code over GF(2) with n=512, k=16 and d=224.
This code was found by Heurico 1.16 in 49.9 seconds.