The generator matrix

 1  1  1  X  1
 0  X 2X  X  0
 0  0 X^2  0 X^2
 0  0  0 2X^2 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+38x^6+324x^8+92x^9+972x^10+648x^11+102x^12+10x^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 0.000568 seconds.