The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+10x^3+108x^4+580x^6+648x^7+4374x^8+2240x^9+39204x^10+8748x^11+2240x^12+864x^13+32x^15

The gray image is a linear code over GF(3) with n=45, k=10 and d=9.
This code was found by Heurico 1.16 in 0.0917 seconds.