The generator matrix

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

generates a code of length 12 over Z3[X]/(X^3) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+264x^20+70x^21+942x^22+816x^23+1720x^24+1788x^25+816x^26+68x^27+24x^28+48x^29+2x^30+2x^33

The gray image is a linear code over GF(3) with n=108, k=8 and d=60.
This code was found by Heurico 1.16 in 0.0156 seconds.