The generator matrix

 1  0  1
 0  1 2X+1

generates a code of length 3 over Z3[X]/(X^2) who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+18x^4+24x^6+36x^7+2x^9

The gray image is a linear code over GF(3) with n=9, k=4 and d=4.
This code was found by Heurico 1.16 in 2.72e-005 seconds.