The generator matrix

 1  0  1  1  1  6  1  1  8  1 14  1 10  1  1  1  1  0  1  1 14  0  1  1  1  1  0  1 14  0  1  1  1  4  1  1  1  1  4  1 12  1  1  1  1  8  4  1  2 12  1  0 14  1  1 10  1  6  1  1  6  2  4  1
 0  1 11  6  1  1  0 11  1  6  1 13  1  0  3  5  6  1 15  8  1  1 13  2 12  5  1  3  1  1  5 14  8  1 13  2  1 13  1  2  1  9  4 14  3  1  1  9  4  1  5  1  1  2  7  1  4  1  7  0  1 10  0  5
 0  0 12  0  0  0  0  0  0  8  8  4  0  4 12 12  0 12  8  8  4  4  8  4  0  4  8 12  0 12  8  4 12  4  0  4  4  0 12  8  4  4  8  0  8  0 12  0  0 12  8 12  8 12 12  4  0  0  8 12  0  4  4 12
 0  0  0 12  0  0 12  8  4  8 12  0  8  0  8  8 12  4  8  0  8  8 12 12 12  4 12  4  0  4  4  8  4  4  8 12  8  8  0  4  8 12  0  0  8 12  4  4  8  0 12  0 12  8  8  0  4  4 12  4  8  4  8  0
 0  0  0  0  4  0  0 12  8  0  8  0  0  4  4 12  4  0  0  4  8 12  8  4  4  8 12  0  4  4  4  8  4 12  0  4  8 12  0  0  4  8 12 12  8  8  0 12  4  4  8  8  0  8  0  4  8  4  0  8  8  0 12 12
 0  0  0  0  0  8  0  0  8  0  8  0  8  0  8  8  8  0  8  8  0  8  8  0  8  0  0  0  8  0  8  0  8  0  0  0  8  8  8  8  0  8  0  0  8  0  8  8  0  0  0  8  0  8  8  0  0  0  8  0  0  8  8  0
 0  0  0  0  0  0  8  8  0  8  8  8  8  0  8  0  8  8  0  0  0  0  0  0  0  0  0  8  0  0  0  8  8  8  0  8  8  8  8  8  0  8  8  0  8  0  0  8  0  8  0  0  8  8  0  0  0  8  0  0  0  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+62x^54+152x^55+256x^56+568x^57+959x^58+1586x^59+3240x^60+5236x^61+7249x^62+8708x^63+9476x^64+9316x^65+7036x^66+4860x^67+3120x^68+1630x^69+1015x^70+512x^71+198x^72+116x^73+109x^74+50x^75+24x^76+28x^77+17x^78+4x^79+5x^80+2x^85+1x^86

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 52.4 seconds.