The generator matrix

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

generates a code of length 11 over Z3[X]/(X^3) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+72x^16+516x^18+432x^19+2916x^20+1488x^21+6210x^22+5832x^23+1548x^24+576x^25+86x^27+6x^30

The gray image is a linear code over GF(3) with n=99, k=9 and d=48.
This code was found by Heurico 1.16 in 8.97 seconds.