The generator matrix

 1  1  1  1
 0  X 2X X^2

generates a code of length 4 over Z3[X]/(X^3) who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+14x^6+12x^7+180x^8+28x^9+6x^10+2x^12

The gray image is a linear code over GF(3) with n=36, k=5 and d=18.
This code was found by Heurico 1.16 in 6.82e-005 seconds.