The generator matrix

 1  1  1  1  2  1  1
 0  2  0  0  6  0  0
 0  0  2  0  2  0  0
 0  0  0  2  2  0  0
 0  0  0  0  8  0  0
 0  0  0  0  0  8  0
 0  0  0  0  0  0  8

generates a code of length 7 over Z16 who´s minimum homogenous weight is 2.

Homogenous weight enumerator: w(x)=1x^0+79x^2+192x^3+909x^4+1920x^5+11811x^6+35712x^7+11811x^8+1920x^9+909x^10+192x^11+79x^12+1x^14

The gray image is a code over GF(2) with n=56, k=16 and d=8.
This code was found by Heurico 1.16 in 0.413 seconds.