The generator matrix

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

generates a code of length 11 over Z3[X]/(X^2) who´s minimum homogenous weight is 15.

Homogenous weight enumerator: w(x)=1x^0+96x^15+162x^16+360x^18+972x^19+720x^21+1944x^22+750x^24+1296x^25+242x^27+18x^30

The gray image is a linear code over GF(3) with n=33, k=8 and d=15.
This code was found by Heurico 1.16 in 0.0514 seconds.