The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+65x^56+396x^57+1089x^58+2090x^59+4013x^60+5122x^61+7133x^62+8300x^63+9062x^64+8380x^65+7737x^66+5022x^67+3461x^68+1976x^69+962x^70+362x^71+210x^72+50x^73+35x^74+26x^75+18x^76+10x^77+1x^78+6x^79+2x^80+2x^81+3x^82+2x^83

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 38.6 seconds.