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  4  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  0  1  1
 0  2  0  2  0  0  2  2  4  6  4  6 12 14 12 14 12 14 12  6  8 10  8 10  8  2 10 12  6  4  8 14  2  4  0 10  0  2 14 12 10  4  6  8 14  0 10 14  4  8 10 12 14  0  6  8  2  8  2 12  6  4  6  4 10  4  2  0  0
 0  0  2  2 12  6 14  4  4  6 10  8 14 10  8 12 12 14  2  4  8 10 14  8  4 10  6  6  2  0  2  0 12 14 10 12  8 10  4  0 14  2  0 12  6 14  0  2 12  0  2 10  8  4 12 10  6  6  8  4 14  8 10  6  4  2  0  0  6

generates a code of length 69 over Z16 who´s minimum homogenous weight is 67.

Homogenous weight enumerator: w(x)=1x^0+72x^67+193x^68+496x^69+184x^70+72x^71+5x^72+1x^132

The gray image is a code over GF(2) with n=552, k=10 and d=268.
This code was found by Heurico 1.16 in 8.4 seconds.