The generator matrix

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

generates a code of length 12 over Z3[X]/(X^2) who´s minimum homogenous weight is 21.

Homogenous weight enumerator: w(x)=1x^0+24x^21+90x^22+30x^24+36x^25+24x^27+36x^28+2x^36

The gray image is a linear code over GF(3) with n=36, k=5 and d=21.
This code was found by Heurico 1.16 in 0.000508 seconds.