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  1  1  1  1  1  1  1  1  1  2  2  1  2  2  1  4  4  1  1  1  2  1  2  2  1  4  1  1  2  1  1  2
 0 12  0  0  0  0  0  0  0  4 12 12  4  8  8 12  8  0 12 12  4  4  0 12  8  4 12  4 12  0 12  8  8  0 12  8  0  8  8  0 12  8  4 12  0  8  4  8 12  0  4  8  4 12  8  0  8  4  0  4  4 12  4  0
 0  0 12  0  0  0  4 12 12  4  4  0  8  0 12 12 12  8  8 12  4 12 12  0  0  4 12  8  0  4  8  0  8  0 12  8  0 12  0  8  8  4  4  0  4  4  8 12  8  8  4  0 12  0  8  4  8  4 12 12 12  0  0  8
 0  0  0 12  0  4  4  4  0  8  0  8 12  0  0 12 12  8  4 12 12  0  4  4 12  0  4  8  8  8  4  4  4  0 12  0  4 12  4  0  0  4  4 12 12 12  8  8 12 12  8  4  8  4  4  4  0  0  4 12  8  0 12 12
 0  0  0  0 12  4  8  4  4  0  4  4  0  0  8  4 12 12  4  4  8  4  0  8  4  0  8 12  8 12 12  0  0  0  8 12 12  0  4  0  4  4  4  8  0  4 12 12 12  4  4  4  0  4  8 12  8  0  8  0  8  8  0 12
 0  0  0  0  0  8  8  0  8  8  8  0  8  8  8  8  8  8  0  0  8  0  0  0  0  0  0  8  8  0  8  8  0  8  0  0  0  0  8  0  0  8  8  8  0  8  0  0  0  8  8  0  0  0  8  8  0  0  0  8  8  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+203x^56+12x^57+256x^58+32x^59+391x^60+244x^61+830x^62+1216x^63+1826x^64+1300x^65+866x^66+224x^67+290x^68+44x^69+222x^70+136x^72+54x^74+31x^76+12x^78+1x^80+1x^104

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 67.7 seconds.