The generator matrix

 1  0  0  1
 0  1  0 2X^2+2X+1
 0  0  1 2X^2+2X+2
 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+432x^4+6072x^6+1728x^7+36936x^8+12128x^9+1728x^10+16x^12

The gray image is a linear code over GF(3) with n=36, k=10 and d=9.
This code was found by Heurico 1.16 in 0.0685 seconds.