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

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

Homogenous weight enumerator: w(x)=1x^0+190x^56+8x^57+254x^58+56x^59+420x^60+424x^61+698x^62+1048x^63+2105x^64+1048x^65+718x^66+424x^67+305x^68+56x^69+166x^70+8x^71+136x^72+76x^74+34x^76+8x^78+8x^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 92.2 seconds.