The generator matrix

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

generates a code of length 22 over Z3[X]/(X^3) who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+126x^36+246x^37+216x^38+318x^39+684x^40+216x^41+2440x^42+1428x^43+6318x^44+4542x^45+1464x^46+432x^47+426x^48+486x^49+108x^50+148x^51+66x^52+2x^54+12x^57+4x^60

The gray image is a linear code over GF(3) with n=198, k=9 and d=108.
This code was found by Heurico 1.16 in 0.631 seconds.