The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+6x^4+48x^6+24x^7+540x^8+80x^9+24x^10+6x^12

The gray image is a linear code over GF(3) with n=36, k=6 and d=12.
This code was found by Heurico 1.16 in 8.11e-005 seconds.