The generator matrix
1 0 1 1 1 1 1 1 1 1 1
0 1 1 2 2X+1 0 X 2X+1 X X+1 0
0 0 2X 0 X X 2X 0 X 2X 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+66x^20+20x^21+84x^23+18x^24+12x^26+14x^27+4x^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 0.000414 seconds.