The generator matrix

 1  0  1
 0  1  2
 0  0  1

generates a code of length 3 over Z8 who´s minimum homogenous weight is 1.

Homogenous weight enumerator: w(x)=1x^0+18x^1+111x^2+252x^3+111x^4+18x^5+1x^6

The gray image is a code over GF(2) with n=12, k=9 and d=2.
This code was found by Heurico 1.16 in 7.41e-005 seconds.