The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+8x^3+108x^4+240x^6+432x^7+4860x^8+464x^9+432x^10+16x^12

The gray image is a linear code over GF(3) with n=36, k=8 and d=9.
This code was found by Heurico 1.16 in 0.00222 seconds.