The generator matrix
1 1 1 1 1
0 X 0 0 2X^2+X
0 0 X 0 2X^2+2X
0 0 0 X 2X^2+2X
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+60x^4+200x^6+360x^7+810x^8+740x^9+14652x^10+1620x^11+750x^12+480x^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 0.02 seconds.