The generator matrix

 1  0  1  1
 0  1 2X^2+2X+1  0
 0  0 2X^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+24x^4+156x^6+96x^7+1512x^8+296x^9+96x^10+6x^12

The gray image is a linear code over GF(3) with n=36, k=7 and d=12.
This code was found by Heurico 1.16 in 0.000201 seconds.