The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+76x^56+226x^57+593x^58+1084x^59+1694x^60+2714x^61+3555x^62+4190x^63+4636x^64+4446x^65+3568x^66+2384x^67+1608x^68+976x^69+465x^70+276x^71+119x^72+48x^73+38x^74+30x^75+21x^76+2x^77+4x^78+2x^79+4x^81+1x^82+2x^83+5x^84

The gray image is a code over GF(2) with n=512, k=15 and d=224.
This code was found by Heurico 1.16 in 12.9 seconds.