The generator matrix
1 1 1 1 1 1 1 1 1 X X 1
0 X 2X X^2 2X^2+X X^2+2X 2X^2 X^2+X 2X^2+2X 2X^2+X 2X 0
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+42x^22+12x^23+92x^24+84x^25+6x^26+4x^27+2x^30
The gray image is a linear code over GF(3) with n=108, k=5 and d=66.
This code was found by Heurico 1.16 in 0.000379 seconds.