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

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

Homogenous weight enumerator: w(x)=1x^0+31x^64+60x^65+99x^66+256x^67+612x^68+464x^69+60x^70+824x^71+560x^72+576x^73+52x^74+160x^75+40x^76+160x^77+36x^78+24x^79+32x^80+20x^81+8x^82+16x^83+4x^84+1x^130

The gray image is a code over GF(2) with n=568, k=12 and d=256.
This code was found by Heurico 1.16 in 0.68 seconds.