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

generates a code of length 64 over Z16 who´s minimum homogenous weight is 55.

Homogenous weight enumerator: w(x)=1x^0+80x^55+334x^56+330x^57+888x^58+998x^59+1866x^60+2284x^61+3811x^62+3416x^63+4709x^64+3732x^65+3800x^66+2152x^67+1879x^68+936x^69+751x^70+230x^71+268x^72+118x^73+88x^74+32x^75+22x^76+20x^77+5x^78+2x^79+8x^80+4x^81+2x^83+1x^84+1x^86

The gray image is a code over GF(2) with n=512, k=15 and d=220.
This code was found by Heurico 1.16 in 19.5 seconds.