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  2  1  2  1  1  2  1  1  2  1  1  2  1  1  4  1  1  1  1  1  2  1  2  1  1  2  1  1  1  1  1
 0 12  0  4  0  0  4 12  8 12  0 12  0 12  8 12  8  8  4  4 12 12  0  0 12  4  0  8  4  8  0 12  0  8  4 12  0  0 12 12  0  8 12 12 12  8  8  4  4  4  4  8  0  0 12  0  4 12 12  4  4  8  0  8  4  0 12 12  4  8  4
 0  0 12  4  0 12  4  8  4  4  0  0  0  4  4  8  4  8 12  8 12  8  8  4  8  8  8 12  4  8 12  4  0  4  4  0  0 12  4  8  8  4  0  8 12  0  0  4  4  0  8  8  0  4  0  0  0  4 12  8 12 12 12  8 12 12  0  8  8  4 12
 0  0  0  8  0  0  0  0  0  8  8  0  8  0  8  8  8  0  0  0  8  8  8  8  8  8  8  0  0  0  8  8  0  0  0  0  0  0  0  0  0  0  8  8  8  8  8  0  8  0  8  8  8  8  8  0  0  8  0  8  0  8  8  8  8  0  8  8  0  0  8
 0  0  0  0  8  0  0  8  8  8  8  0  0  8  8  8  0  0  0  8  0  0  0  0  8  0  8  8  8  8  8  8  0  0  0  0  0  0  0  0  8  8  8  8  0  0  0  8  8  8  0  0  0  0  8  8  0  0  0  8  8  8  8  8  8  0  0  0  0  0  8
 0  0  0  0  0  8  0  0  8  0  8  8  0  8  0  0  8  8  8  8  8  8  8  0  8  0  0  0  0  8  8  8  0  0  0  0  8  8  8  8  0  8  0  0  0  8  0  0  0  8  0  8  8  8  0  8  0  0  8  8  8  0  0  0  0  8  0  0  0  8  0
 0  0  0  0  0  0  8  0  0  0  8  0  8  8  8  8  8  0  8  0  0  8  8  8  8  8  8  0  8  0  8  0  8  8  0  8  8  8  0  8  8  8  0  0  8  0  0  0  0  8  0  0  0  0  0  8  0  8  0  8  8  0  0  0  0  0  0  8  8  8  8

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

Homogenous weight enumerator: w(x)=1x^0+170x^64+84x^66+311x^68+1000x^70+1024x^71+1079x^72+164x^74+123x^76+20x^78+77x^80+8x^82+29x^84+4x^86+1x^88+1x^124

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 6.39 seconds.