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  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  1  1  1  1  2  2
 0 12  0  4  0  0  4 12  0  0  4 12  0  0  4 12  8  8 12  4  8  8 12  4  8  8 12  4  8  8 12  4  8  0 12  4  4  4 12  4  8  0  4  4  0  0  8  8 12  4  8  0 12 12  8  0 12 12 12  4  0  0  8  8  0  8  4 12  8  0
 0  0 12  4  0 12  4  0  8  4 12  8  8  4 12  8  8  4 12  8  8  4 12  8  0 12  4  0  0 12  4  0  4 12  0  8  4 12  0  8  4 12  4 12  0  8  8  0  8  0 12  4 12  4 12  4 12  4  8  0  0  8  8  0  0  4  4  0  4 12
 0  0  0  8  8  8  0  8  8  8  8  8  0  0  0  0  0  0  0  0  8  8  8  8  8  8  8  8  0  0  0  0  0  0  0  0  8  8  8  8  8  8  0  0  8  8  8  8  8  8  8  8  8  8  0  0  0  0  0  0  0  0  0  0  0  0  0  8  8  0

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

Homogenous weight enumerator: w(x)=1x^0+54x^68+404x^70+47x^72+4x^74+2x^104

The gray image is a code over GF(2) with n=560, k=9 and d=272.
This code was found by Heurico 1.16 in 0.357 seconds.