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

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

Homogenous weight enumerator: w(x)=1x^0+27x^56+58x^58+30x^60+256x^63+1305x^64+256x^65+44x^66+18x^68+11x^72+26x^74+15x^76+1x^124

The gray image is a code over GF(2) with n=512, k=11 and d=224.
This code was found by Heurico 1.16 in 0.257 seconds.