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

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

Homogenous weight enumerator: w(x)=1x^0+177x^64+92x^65+434x^66+396x^67+724x^68+820x^69+1026x^70+992x^71+1033x^72+824x^73+674x^74+332x^75+297x^76+116x^77+138x^78+8x^79+43x^80+4x^81+28x^82+23x^84+4x^86+5x^88+1x^104

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 1.8 seconds.