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

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

Homogenous weight enumerator: w(x)=1x^0+141x^64+132x^65+280x^66+258x^67+371x^68+708x^69+491x^70+562x^71+396x^72+246x^73+208x^74+102x^75+112x^76+26x^77+35x^78+6x^79+2x^80+6x^81+4x^82+1x^84+2x^85+5x^86+1x^110

The gray image is a code over GF(2) with n=560, k=12 and d=256.
This code was found by Heurico 1.16 in 0.835 seconds.