The generator matrix

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

generates a code of length 11 over Z3[X]/(X^3) who´s minimum homogenous weight is 18.

Homogenous weight enumerator: w(x)=1x^0+28x^18+30x^20+48x^21+540x^22+12x^23+40x^24+12x^26+16x^27+2x^33

The gray image is a linear code over GF(3) with n=99, k=6 and d=54.
This code was found by Heurico 1.16 in 0.000769 seconds.