The generator matrix

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

generates a code of length 5 over Z3[X]/(X^3) who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+36x^4+200x^6+216x^7+1458x^8+740x^9+13068x^10+2916x^11+750x^12+288x^13+10x^15

The gray image is a linear code over GF(3) with n=45, k=9 and d=12.
This code was found by Heurico 1.16 in 0.0114 seconds.