The generator matrix

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

generates a code of length 12 over Z3[X]/(X^3) who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+186x^22+48x^23+92x^24+372x^25+24x^26+4x^27+2x^30

The gray image is a linear code over GF(3) with n=108, k=6 and d=66.
This code was found by Heurico 1.16 in 0.000504 seconds.