The generator matrix

 1  0  1  1  6  1  1  1  6  1 12  1  4  1  1  1 14  1 10  1  1  1  0  1  1  1  2  1  1 14  1  1  2  1  1  8  1  1  1  1  2  1  4  1  1  1 12  2  1 10  1  4 10  1  0  1 12  8  0  1  1  1  1  1  1  1 14  1  8  1  1
 0  1  1  6  1  3  5  4  1  2  1  7  1 12  9 15  1 10  1 11 12  6  1 13  5 15  1  4  1  1  8 10  1  1  8  1 15 14 12 15  1  3  1 15  5  2  1  1 10  1  8  1  1  7  1  0 12  1  2  5 10  6 12 15 12  3  1  8  2  9  8
 0  0  2  0  0  8  8 10  6 10 14  2 10 14  6  8  2 14  0  2  0  4 12  4  4  6  0  4  8 12  0  6  2  2 10 14 12  4  6  4  4  6  2  0 14 12  8 12  4 14  4  4  2  8  0 10  2 14 10 12  8 14  6  4  0 12  2 14 14 10 12
 0  0  0  8  0  8  0  0  8  8  0  8  0  0  0  0  8  8  8  8  8  8  0  8  0  8  8  8  0  0  0  0  8  0  0  8  0  0  8  8  8  0  8  0  8  8  8  0  0  0  8  0  8  8  8  8  8  0  0  8  0  0  8  8  0  8  0  0  0  8  8
 0  0  0  0  8  0  8  0  0  8  8  0  0  8  8  0  8  0  0  8  8  0  0  8  8  0  8  8  0  8  8  0  0  8  8  8  0  0  8  0  0  8  0  8  8  8  8  0  8  8  0  8  8  8  0  0  8  0  8  0  0  8  0  8  0  8  0  0  0  8  8

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

Homogenous weight enumerator: w(x)=1x^0+346x^66+448x^67+1136x^68+708x^69+1206x^70+824x^71+1185x^72+712x^73+770x^74+292x^75+330x^76+68x^77+88x^78+25x^80+16x^81+16x^82+4x^83+8x^84+6x^86+1x^88+2x^92

The gray image is a code over GF(2) with n=568, k=13 and d=264.
This code was found by Heurico 1.16 in 1.81 seconds.