The generator matrix

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

generates a code of length 5 over Z3[X]/(X^3) who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+36x^8+14x^9+108x^10+72x^11+12x^12

The gray image is a linear code over GF(3) with n=45, k=5 and d=24.
This code was found by Heurico 1.16 in 9.2e-005 seconds.