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

generates a code of length 71 over Z16 who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+55x^64+184x^65+267x^66+538x^67+708x^68+856x^69+1156x^70+1082x^71+1006x^72+806x^73+532x^74+358x^75+194x^76+182x^77+99x^78+58x^79+50x^80+18x^81+23x^82+8x^83+2x^84+2x^85+4x^87+2x^90+1x^110

The gray image is a code over GF(2) with n=568, k=13 and d=256.
This code was found by Heurico 1.16 in 1.67 seconds.