The generator matrix

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

generates a code of length 12 over Z3[X]/(X^2) who´s minimum homogenous weight is 15.

Homogenous weight enumerator: w(x)=1x^0+102x^15+102x^16+126x^17+540x^18+426x^19+612x^20+2112x^21+1308x^22+1620x^23+4968x^24+1572x^25+1710x^26+2936x^27+924x^28+306x^29+264x^30+42x^31+6x^33+6x^36

The gray image is a linear code over GF(3) with n=36, k=9 and d=15.
This code was found by Heurico 1.16 in 0.563 seconds.