The generator matrix

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

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+56x^36+12x^37+234x^38+190x^39+726x^40+1044x^41+2706x^42+2772x^43+2106x^44+5242x^45+2760x^46+1440x^47+238x^48+48x^49+36x^50+42x^51+18x^54+4x^57+6x^60+2x^63

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 0.304 seconds.