The generator matrix

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

generates a code of length 11 over Z3[X]/(X^2) who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+72x^6+186x^9+828x^12+1764x^15+3108x^18+4284x^21+39366x^22+4302x^24+3266x^27+1530x^30+342x^33

The gray image is a linear code over GF(3) with n=33, k=10 and d=6.
This code was found by Heurico 1.16 in 0.785 seconds.