The generator matrix

 1  1  1
 0  X 2X^2
 0  0 2X^2+X

generates a code of length 3 over Z3[X]/(X^3) who´s minimum homogenous weight is 2.

Homogenous weight enumerator: w(x)=1x^0+18x^2+6x^3+108x^4+72x^5+1686x^6+216x^7+72x^8+8x^9

The gray image is a linear code over GF(3) with n=27, k=7 and d=6.
This code was found by Heurico 1.16 in 0.000157 seconds.