The generator matrix

 1  1  1  1  1
 0  X  0 2X^2+X  0
 0  0  X X^2+2X  0
 0  0  0 X^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+18x^4+92x^6+108x^7+162x^8+308x^9+5076x^10+324x^11+318x^12+144x^13+10x^15

The gray image is a linear code over GF(3) with n=45, k=8 and d=12.
This code was found by Heurico 1.16 in 0.00248 seconds.