The generator matrix

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

generates a code of length 5 over Z3[X]/(X^2) who´s minimum homogenous weight is 3.

Homogenous weight enumerator: w(x)=1x^0+10x^3+180x^4+580x^6+1080x^7+2430x^8+2240x^9+4590x^10+4860x^11+2240x^12+1440x^13+32x^15

The gray image is a linear code over GF(3) with n=15, k=9 and d=3.
This code was found by Heurico 1.16 in 0.0232 seconds.