The generator matrix
1 1 1 1 1 1 1 X X 1 1 1
0 X 2X 0 2X^2+X 2X 0 2X^2+X 2X 0 X^2 X^2
0 0 X^2 0 0 X^2 X^2 2X^2 0 X^2 2X^2 2X^2
0 0 0 X^2 0 2X^2 X^2 X^2 2X^2 0 2X^2 2X^2
0 0 0 0 2X^2 2X^2 0 2X^2 2X^2 X^2 X^2 2X^2
generates a code of length 12 over Z3[X]/(X^3) who´s minimum homogenous weight is 18.
Homogenous weight enumerator: w(x)=1x^0+108x^18+162x^20+168x^21+972x^22+648x^23+1638x^24+1944x^25+648x^26+152x^27+120x^30
The gray image is a linear code over GF(3) with n=108, k=8 and d=54.
This code was found by Heurico 1.16 in 0.026 seconds.