The generator matrix

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

generates a code of length 23 over Z3[X]/(X^3) who´s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+222x^38+170x^39+654x^41+602x^42+2910x^44+1232x^45+5832x^46+5208x^47+1232x^48+948x^50+326x^51+258x^53+52x^54+6x^56+20x^57+8x^60+2x^63

The gray image is a linear code over GF(3) with n=207, k=9 and d=114.
This code was found by Heurico 1.16 in 12.9 seconds.