The generator matrix

 1  1  1  1  1  1  1  1  X  X  1  1
 0  X  0  0 2X 2X^2+X X^2 2X 2X^2  X  X X^2
 0  0  X 2X  0 2X^2+2X 2X^2 X^2 2X^2+X 2X^2+X  X X^2
 0  0  0 X^2 2X^2 2X^2 X^2  0  0  0 2X^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+60x^18+54x^19+222x^20+162x^21+810x^22+576x^23+2214x^24+1458x^25+612x^26+182x^27+108x^28+48x^29+54x^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 0.0249 seconds.