The generator matrix

 1  1  1  1  1  1  1  1  1 2X^2 2X^2
 0  X  0  0 2X 2X^2+X  X 2X^2+2X 2X  X  X
 0  0  X 2X  0 2X^2+2X  X 2X^2+X 2X 2X^2+X 2X^2+X
 0  0  0 X^2 2X^2 2X^2 2X^2  0 2X^2 2X^2 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+54x^16+354x^18+324x^19+840x^21+3564x^22+900x^24+432x^25+86x^27+6x^30

The gray image is a linear code over GF(3) with n=99, k=8 and d=48.
This code was found by Heurico 1.16 in 0.022 seconds.