The generator matrix

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

generates a code of length 4 over Z3[X]/(X^3) who´s minimum homogenous weight is 2.

Homogenous weight enumerator: w(x)=1x^0+42x^2+8x^3+540x^4+252x^5+4290x^6+2160x^7+40680x^8+8564x^9+2160x^10+336x^11+16x^12

The gray image is a linear code over GF(3) with n=36, k=10 and d=6.
This code was found by Heurico 1.16 in 0.047 seconds.