The generator matrix

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

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+304x^36+390x^37+2058x^38+2980x^39+6894x^40+9684x^41+18736x^42+24030x^43+34656x^44+33164x^45+24504x^46+12990x^47+5192x^48+1008x^49+360x^50+128x^51+36x^52+30x^53+2x^54

The gray image is a linear code over GF(3) with n=198, k=11 and d=108.
This code was found by Heurico 1.16 in 17.1 seconds.