The generator matrix

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

generates a code of length 16 over Z16 who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+125x^16+2x^24

The gray image is a code over GF(2) with n=128, k=7 and d=64.
This code was found by Heurico 1.16 in 0.00146 seconds.