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  1  1  1  1  1  1  1  2  1  2  1  4  2  4  1  4  2  1  1  4  4  4  1  4  0  1  2  8  1  2  2  1  1  1  4  1  1
 0 12  0  0  0  0  0  0  0 12  4 12 12  4  8  8  8 12 12 12  4  8 12  4  4  0 12  0 12  0  8 12  4  0  0  4  8  8  4 12  0  0  8  8  8 12  0  0 12  8  4  4  4  4  4  8  4  4  8  8  4 12  4  0
 0  0 12  0  0  0  4 12  4  4  4  8  0  8  4  4  8 12 12  0  8  4  0  0 12  4  4 12 12  8 12 12  8  8  8  4  4  8  4 12  4  8  0 12  4  0  4 12  0 12  4 12  4 12  4 12  0  0 12 12 12  0  4  4
 0  0  0 12  0  4  4  4  8  4  0 12  4  8 12  0  8  4  8  4  0  0  4 12  0  0  4 12 12  4  4  4 12 12 12  4  4  0  8 12  4  4 12 12 12  8  0 12 12  0 12 12 12  4 12  0  0 12  4  0  4 12  8 12
 0  0  0  0 12  4  0  4  4  8  0  8 12  4  8  0  4  4  0  8  8 12  4  4 12  8  4 12  8 12  0  4  0  8 12  8 12  8  8  0  0 12  4  8  0 12  4  4  4  0 12  0  4  0  4  0  8  8  0  4  0 12  4  0
 0  0  0  0  0  8  0  0  8  0  8  8  8  0  8  8  8  8  0  8  0  0  0  8  8  0  0  8  8  0  0  8  0  8  0  0  0  8  0  0  8  0  0  0  0  8  8  8  0  8  0  8  8  0  0  8  0  0  8  0  0  8  8  0
 0  0  0  0  0  0  8  0  0  0  0  0  0  8  0  8  8  8  0  8  8  0  8  8  0  8  0  8  8  0  0  0  8  8  8  8  0  0  0  0  0  8  0  8  0  8  0  0  8  8  0  0  8  8  8  0  0  8  8  0  0  0  0  8

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

Homogenous weight enumerator: w(x)=1x^0+70x^54+104x^55+158x^56+288x^57+340x^58+536x^59+767x^60+1044x^61+1653x^62+2162x^63+2315x^64+2110x^65+1655x^66+1036x^67+674x^68+566x^69+274x^70+204x^71+134x^72+78x^73+82x^74+52x^75+47x^76+6x^77+18x^78+2x^79+4x^81+3x^82+1x^94

The gray image is a code over GF(2) with n=512, k=14 and d=216.
This code was found by Heurico 1.16 in 7.39 seconds.