The generator matrix

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

generates a code of length 23 over Z3[X]/(X^3) who´s minimum homogenous weight is 39.

Homogenous weight enumerator: w(x)=1x^0+176x^39+456x^42+486x^44+490x^45+2916x^46+972x^47+704x^48+276x^51+54x^54+20x^57+6x^60+4x^63

The gray image is a linear code over GF(3) with n=207, k=8 and d=117.
This code was found by Heurico 1.16 in 0.0752 seconds.