The generator matrix
1 1 1 1
0 X^2 2X^2 0
generates a code of length 4 over Z3[X]/(X^3) who´s minimum homogenous weight is 6.
Homogenous weight enumerator: w(x)=1x^0+2x^6+72x^8+4x^9+2x^12
The gray image is a linear code over GF(3) with n=36, k=4 and d=18.
This code was found by Heurico 1.16 in 3.6e-005 seconds.