The generator matrix

 1  0  1  1  6  1  1  1  6  1 12  1  1  8  1 12  1  1  2  1  1  1 10  1  4  1  1  1  1  8  1  1  1 10  2  1  1  1  1  1 14  1 12 10  1  1  0  1  1  1  1  1 12  1 14  1  4  1 12 12  1  2  6 10  1 14  0  1  1  1
 0  1  1  6  1  3  5  4  1  2  1  7 13  1  4  1 14 11  1 10  7  8  1 11  1  6  7  9  9  1 12 10  9  1  1  0  4  6 13  7  1 15  2  1  9 12  1 10  6  4  4  3  1  1  1 10  1  8  1  1  1  2  1  1  6  1  1  2 10  0
 0  0  2  0  0  8  8 10  6 10 14 10  2  4 12  2 12  2 10 14  4  2  0 12 12 10  6  8 12  2  0  8 14  6  4  0  6 12 10  8  4  6 10  2  8  4  6  6  2 14  4  0  4 12 10  0 10 14  0 10  4  2  4 10  4 14 14  2  2  0
 0  0  0  8  0  8  0  0  8  8  0  0  8  8  8  8  0  8  0  8  8  0  8  0  0  8  8  8  0  8  8  0  8  0  0  0  0  8  0  0  8  0  0  8  0  0  8  0  0  8  8  0  0  8  8  8  0  0  8  0  8  0  0  8  8  0  8  0  8  0
 0  0  0  0  8  0  8  0  0  8  8  8  0  0  8  8  8  8  0  0  8  8  8  0  0  0  8  0  8  0  8  0  8  8  0  8  0  8  8  0  0  0  0  0  0  8  8  8  0  8  0  8  8  0  8  8  8  8  8  0  8  8  8  8  0  0  8  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+52x^64+342x^65+441x^66+1058x^67+751x^68+1042x^69+957x^70+1294x^71+638x^72+696x^73+356x^74+306x^75+97x^76+86x^77+14x^78+22x^79+12x^80+10x^81+6x^82+8x^83+1x^86+1x^88+1x^98

The gray image is a code over GF(2) with n=560, k=13 and d=256.
This code was found by Heurico 1.16 in 1.11 seconds.