The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+10x^54+66x^55+134x^56+298x^57+522x^58+790x^59+1693x^60+2362x^61+4069x^62+3670x^63+5634x^64+3674x^65+4101x^66+2346x^67+1636x^68+762x^69+463x^70+268x^71+88x^72+68x^73+26x^74+24x^75+23x^76+4x^77+17x^78+4x^79+5x^80+7x^82+1x^86+2x^88

The gray image is a code over GF(2) with n=512, k=15 and d=216.
This code was found by Heurico 1.16 in 13.7 seconds.