The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+65x^56+394x^57+1160x^58+1920x^59+3467x^60+5060x^61+7473x^62+8786x^63+9559x^64+8158x^65+7472x^66+5118x^67+3440x^68+1846x^69+882x^70+348x^71+219x^72+86x^73+32x^74+14x^75+13x^76+2x^77+5x^78+6x^79+4x^80+6x^81

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 38.7 seconds.