The generator matrix

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

generates a code of length 22 over Z3[X]/(X^3) who´s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+732x^38+1270x^39+2322x^40+3720x^41+5282x^42+7884x^43+13386x^44+9332x^45+8046x^46+4830x^47+1788x^48+216x^49+168x^50+64x^51+6x^53+2x^57

The gray image is a linear code over GF(3) with n=198, k=10 and d=114.
This code was found by Heurico 1.16 in 3.94 seconds.