The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+92x^2+394x^3+1238x^4+1656x^5+10445x^6+37884x^7+10445x^8+1656x^9+1238x^10+394x^11+92x^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 0.242 seconds.