The generator matrix

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

generates a code of length 12 over Z3[X]/(X^2) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+84x^20+70x^21+78x^22+96x^23+100x^24+60x^25+96x^26+68x^27+24x^28+48x^29+2x^30+2x^33

The gray image is a linear code over GF(3) with n=36, k=6 and d=20.
This code was found by Heurico 1.16 in 0.00536 seconds.