The generator matrix

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

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+18x^4+40x^6+108x^7+324x^8+80x^9+702x^10+648x^11+80x^12+144x^13+32x^15

The gray image is a linear code over GF(3) with n=15, k=7 and d=3.
This code was found by Heurico 1.16 in 0.000442 seconds.