The generator matrix

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

generates a code of length 70 over Z16 who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+270x^68+128x^69+224x^70+128x^71+269x^72+2x^76+1x^96+1x^104

The gray image is a code over GF(2) with n=560, k=10 and d=272.
This code was found by Heurico 1.16 in 0.236 seconds.