The generator matrix

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

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+84x^20+26x^21+324x^22+90x^23+1000x^24+432x^25+108x^26+20x^27+54x^28+42x^29+4x^30+2x^33

The gray image is a linear code over GF(3) with n=108, k=7 and d=60.
This code was found by Heurico 1.16 in 0.0165 seconds.