The generator matrix

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

generates a code of length 5 over Z3[X]/(X^3) who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+42x^6+36x^7+54x^8+80x^9+1710x^10+108x^11+114x^12+36x^13+6x^15

The gray image is a linear code over GF(3) with n=45, k=7 and d=18.
This code was found by Heurico 1.16 in 0.000525 seconds.