The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+51x^56+370x^57+1047x^58+2330x^59+3284x^60+5146x^61+7135x^62+8722x^63+9428x^64+8988x^65+6932x^66+5374x^67+3310x^68+1772x^69+852x^70+458x^71+155x^72+86x^73+29x^74+8x^75+22x^76+18x^77+5x^78+4x^79+5x^80+4x^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 38.5 seconds.