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

generates a code of length 64 over Z16 who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+178x^56+16x^57+284x^58+100x^59+397x^60+576x^61+436x^62+1860x^63+566x^64+1872x^65+476x^66+588x^67+291x^68+96x^69+200x^70+12x^71+130x^72+64x^74+31x^76+12x^78+5x^80+1x^100

The gray image is a code over GF(2) with n=512, k=13 and d=224.
This code was found by Heurico 1.16 in 4.41 seconds.