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

generates a code of length 70 over Z16 who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+228x^64+314x^65+598x^66+718x^67+756x^68+1230x^69+878x^70+1192x^71+689x^72+572x^73+336x^74+198x^75+198x^76+78x^77+107x^78+28x^79+28x^80+14x^81+12x^82+8x^83+4x^84+4x^86+1x^102

The gray image is a code over GF(2) with n=560, k=13 and d=256.
This code was found by Heurico 1.16 in 1.46 seconds.