The generator matrix

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

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+894x^36+1896x^37+5154x^38+8620x^39+22806x^40+25152x^41+62158x^42+73488x^43+87354x^44+113004x^45+75180x^46+34446x^47+15204x^48+5400x^49+480x^50+98x^51+78x^52+18x^53+8x^54+2x^57

The gray image is a linear code over GF(3) with n=198, k=12 and d=108.
This code was found by Heurico 1.16 in 139 seconds.