The generator matrix

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

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+390x^15+324x^16+1638x^18+2592x^19+4086x^21+12150x^22+6708x^24+19116x^25+5234x^27+5184x^28+1584x^30+30x^33+12x^36

The gray image is a linear code over GF(3) with n=36, k=10 and d=15.
This code was found by Heurico 1.16 in 2.42 seconds.