The generator matrix
1 1 1 1 1 1 1 1 1 X 1
0 X 0 0 X 0 X X 2X X 0
0 0 X 0 2X X 2X X 2X 0 0
0 0 0 X 2X 2X 0 2X 2X X 0
generates a code of length 11 over Z3[X]/(X^2) who´s minimum homogenous weight is 18.
Homogenous weight enumerator: w(x)=1x^0+24x^18+54x^20+36x^21+108x^23+2x^27+18x^30
The gray image is a linear code over GF(3) with n=33, k=5 and d=18.
This code was found by Heurico 1.16 in 0.000526 seconds.