The generator matrix

 1  1  1  1  1  1  1
 0  2  0  0  0  4  0
 0  0  2  0  0  4  0
 0  0  0  2  0  4  0
 0  0  0  0  2  4  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+318x^3+1238x^4+2920x^5+6605x^6+43188x^7+6605x^8+2920x^9+1238x^10+318x^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 0.349 seconds.