The generator matrix
1 1 1
0 X 2X
generates a code of length 3 over Z3[X]/(X^3) who´s minimum homogenous weight is 4.
Homogenous weight enumerator: w(x)=1x^0+18x^4+186x^6+36x^7+2x^9
The gray image is a linear code over GF(3) with n=27, k=5 and d=12.
This code was found by Heurico 1.16 in 4.41e-005 seconds.