The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  0  1 12  2  1  1  1  1  1  1  1  1  1  1  0  1  1  1  1  2  2  2  8  2  1  4  1  1  1  1  1  1  8  1  4  1  1  8  1  4  2  1  8  1
 0  2  0  6  4  6 12  2  8  6  0  6  4  4  2 10 14  2  0  6  2 12  2 10 12  2  0 14  8  4  6  6  8  2  2 14  8  0  2 14  6 10  2  2  2  2 10 10 14  4  4 12  2 14  2  0 14  2  2  4 14  8  2  0
 0  0 12  0  4  0  0  0  8  4  4 12  8 12  4 12  0  8  0  8  4  8  4  0  4 12  4 12  4  4  4  0 12  0 12  4 12  0  8 12 12 12  0  8 12 12 12  8  4  8  0 12  0  4  0  8  8  8  4  4 12  0 12  0
 0  0  0 12  0  0  8 12 12 12 12  8  4 12  0  4 12 12  8  0 12  0 12  8  4  0  4  8  8  0  4  8  0  8  4 12  4 12 12  8 12  4  4  4  0  0  8  8  8  8  8  0 12  0  4  4 12 12  4  0  0  8  8  0
 0  0  0  0  8  0  8  8  0  8  0  0  8  8  0  8  8  0  8  8  0  0  8  0  8  8  0  8  0  0  0  8  8  0  8  0  8  0  8  8  8  0  8  8  0  8  8  8  0  0  0  8  8  0  0  8  0  0  8  8  8  8  0  0
 0  0  0  0  0  8  0  0  0  8  0  8  0  0  0  0  8  8  8  8  0  8  8  0  8  0  8  8  8  0  0  8  8  8  0  8  0  8  8  0  0  0  8  0  8  8  0  8  8  0  8  0  0  0  0  0  8  0  8  8  0  0  8  0

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

Homogenous weight enumerator: w(x)=1x^0+40x^56+84x^57+193x^58+264x^59+491x^60+596x^61+922x^62+886x^63+1323x^64+876x^65+986x^66+544x^67+410x^68+210x^69+178x^70+84x^71+31x^72+22x^73+13x^74+8x^75+6x^76+2x^77+11x^78+6x^79+1x^80+2x^81+1x^84+1x^94

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 1.55 seconds.