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

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

Homogenous weight enumerator: w(x)=1x^0+87x^68+128x^69+592x^70+128x^71+86x^72+1x^76+1x^136

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 0.363 seconds.