The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  2  1  2  2  0  2  8  2 12  4  2  1  1  2 12  1 12  1  4  2  0  2  2  4 12  8  1  1  1  1  1  2  1  1  1  1
 0  2  0  0  0  2  6 14  4 12  6  2  2 10 12 12 12  8  2  0  6 12  2 12  6 10 10 14 14  4 14  0 12  2  2  2  0  2  0 14 14  4  8  6  2  8  8 12  0  2  0  2  2  2  0  2 10  2  2 10 12  4  0  0
 0  0  2  0  2  2  2  0  8 10  4 14  0  6  2 12  6  2 14  4 12 12  2  4 12 12 10 10  0 10 12 10  4  2 10  0  2  4 10 14  0  2  2  4 10  4  2  4  2  4  2  6  8  4 10  6 10  0 12 12 10  6 10  0
 0  0  0  2  2  0  2  2  2 10 12  8 14 10  8 12  0 14  4 14 10  6 14  8 14 12  2  8  2  4  8  0  2  6 14 12  6 14 14 14  4  8  8 10 12 12  2 14 12  0  4  8 12  2  8  6  8  6  8  8  6  6 10  0
 0  0  0  0  8  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  8  8  8  8  8  8  8  8  8  8  8  8  8  0  8  8  8  8  8  8  8  0  8  8  8  0  8  8  0  8  0  8  8  0  0
 0  0  0  0  0  8  0  0  8  8  8  0  8  8  8  8  8  0  8  8  0  0  8  8  8  0  0  8  8  0  0  0  0  0  8  8  8  8  0  0  0  8  8  0  8  8  8  8  8  0  0  0  8  0  8  8  0  0  8  0  0  8  0  8
 0  0  0  0  0  0  8  8  8  8  0  0  8  8  0  8  8  0  8  0  0  8  0  0  0  8  0  8  0  0  0  8  8  0  0  0  8  0  0  8  8  0  8  0  8  0  0  0  8  8  8  8  8  0  0  8  8  8  0  8  8  0  8  8

generates a code of length 64 over Z16 who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+41x^54+260x^55+497x^56+1132x^57+1207x^58+2574x^59+3146x^60+5078x^61+6380x^62+8264x^63+8156x^64+8516x^65+6587x^66+5184x^67+2957x^68+2512x^69+1185x^70+928x^71+429x^72+288x^73+85x^74+66x^75+40x^76+10x^77+2x^78+4x^79+4x^80+1x^82+1x^84+1x^96

The gray image is a code over GF(2) with n=512, k=16 and d=216.
This code was found by Heurico 1.16 in 68 seconds.