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

generates a code of length 71 over Z16 who´s minimum homogenous weight is 66.

Homogenous weight enumerator: w(x)=1x^0+350x^66+8x^67+507x^68+256x^69+770x^70+496x^71+682x^72+256x^73+386x^74+8x^75+249x^76+86x^78+32x^80+8x^82+1x^120

The gray image is a code over GF(2) with n=568, k=12 and d=264.
This code was found by Heurico 1.16 in 1.08 seconds.