The generator matrix

 1  1  1  1  1  1  1  1  X  X  1
 0  X 2X  0 2X^2+X X^2  0 X^2 2X^2+X 2X 2X
 0  0 X^2  0 X^2  0 X^2 2X^2 X^2  0 X^2
 0  0  0 X^2 2X^2 2X^2 2X^2 2X^2 X^2  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+180x^18+324x^20+180x^21+486x^22+648x^23+306x^24+62x^27

The gray image is a linear code over GF(3) with n=99, k=7 and d=54.
This code was found by Heurico 1.16 in 0.00399 seconds.