The generator matrix

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

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+172x^12+228x^13+948x^14+1544x^15+2136x^16+5448x^17+8310x^18+8616x^19+24456x^20+22288x^21+15918x^22+36096x^23+21938x^24+11364x^25+11616x^26+4730x^27+1104x^28+168x^29+58x^30+8x^33

The gray image is a linear code over GF(3) with n=33, k=11 and d=12.
This code was found by Heurico 1.16 in 23.1 seconds.