The generator matrix
1 1 1 1 1 1 1 1 1 X 1 1
0 X 0 0 X 0 X X 2X X 0 0
0 0 X 0 2X X 2X X 2X 0 0 0
0 0 0 X 2X 2X 0 2X 2X X 0 0
generates a code of length 12 over Z3[X]/(X^2) who´s minimum homogenous weight is 18.
Homogenous weight enumerator: w(x)=1x^0+24x^18+54x^22+36x^24+108x^25+2x^27+18x^33
The gray image is a linear code over GF(3) with n=36, k=5 and d=18.
This code was found by Heurico 1.16 in 0.000533 seconds.