The generator matrix
1 0 1 1 1 1 1 0 1 1 1 0
0 1 1 2 0 1 2 1 0 2X+1 2 1
0 0 2X 0 0 0 0 X X X 2X X
0 0 0 X 0 0 X X X 2X X 0
0 0 0 0 X 0 2X 0 X X X 2X
0 0 0 0 0 2X X 2X X 0 2X 2X
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+480x^18+1296x^21+2592x^24+2168x^27+24x^36
The gray image is a linear code over GF(3) with n=36, k=8 and d=18.
This code was found by Heurico 1.16 in 0.0644 seconds.