The generator matrix

 1  1  1
 0  8  0

generates a code of length 3 over Z16 who´s minimum homogenous weight is 2.

Homogenous weight enumerator: w(x)=1x^0+1x^2+28x^3+1x^4+1x^6

The gray image is a code over GF(2) with n=24, k=5 and d=8.
This code was found by Heurico 1.16 in 4.1e-005 seconds.