The generator matrix

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

generates a code of length 11 over Z3[X]/(X^2) who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+280x^12+90x^14+1718x^15+432x^16+720x^17+5364x^18+2592x^19+4104x^20+9550x^21+6642x^22+6768x^23+11282x^24+3456x^25+1440x^26+4544x^27+52x^30+14x^33

The gray image is a linear code over GF(3) with n=33, k=10 and d=12.
This code was found by Heurico 1.16 in 1.29 seconds.