The generator matrix

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

generates a code of length 11 over Z3[X]/(X^2) who´s minimum homogenous weight is 13.

Homogenous weight enumerator: w(x)=1x^0+90x^13+108x^14+1152x^15+684x^16+864x^17+4074x^18+2844x^19+4050x^20+12888x^21+5418x^22+6372x^23+12078x^24+3690x^25+1728x^26+2594x^27+396x^28+18x^30

The gray image is a linear code over GF(3) with n=33, k=10 and d=13.
This code was found by Heurico 1.16 in 3.77 seconds.