The generator matrix

 1  0  0  1  1
 0  1  0 2X^2+2X+1  0
 0  0  1 2X^2+2X+2  0
 0  0  0 2X^2 X^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+72x^4+740x^6+432x^7+4536x^8+2900x^9+37800x^10+9072x^11+2910x^12+576x^13+10x^15

The gray image is a linear code over GF(3) with n=45, k=10 and d=12.
This code was found by Heurico 1.16 in 0.0725 seconds.