The generator matrix

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

generates a code of length 64 over Z16 who´s minimum homogenous weight is 57.

Homogenous weight enumerator: w(x)=1x^0+128x^57+241x^58+492x^59+965x^60+1282x^61+1740x^62+2120x^63+2310x^64+2390x^65+1830x^66+1238x^67+856x^68+396x^69+184x^70+98x^71+24x^72+16x^73+31x^74+14x^75+3x^76+10x^77+2x^78+6x^79+1x^80+2x^81+2x^82+2x^86

The gray image is a code over GF(2) with n=512, k=14 and d=228.
This code was found by Heurico 1.16 in 83 seconds.