The generator matrix

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

generates a code of length 22 over Z3[X]/(X^3) who´s minimum homogenous weight is 37.

Homogenous weight enumerator: w(x)=1x^0+36x^37+510x^38+1858x^39+1674x^40+2958x^41+8380x^42+5856x^43+10098x^44+14976x^45+5832x^46+3882x^47+2670x^48+180x^49+48x^50+56x^51+30x^52+2x^54+2x^57

The gray image is a linear code over GF(3) with n=198, k=10 and d=111.
This code was found by Heurico 1.16 in 2 seconds.