The generator matrix

 1  0  1  1  1  1  1 2X^2+X  1  1  1  1
 0  1 2X^2+2X+1 2X^2+X  2 X+1 2X^2+X+2  1 2X 2X^2+X 2X^2+2X+1  0
 0  0 2X^2 X^2 2X^2  0 X^2 X^2  0 2X^2 X^2 X^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+72x^20+24x^21+324x^22+294x^23+516x^24+648x^25+276x^26+20x^27+6x^29+6x^30

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 0.00239 seconds.