The generator matrix

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

generates a code of length 23 over Z3[X]/(X^3) who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+216x^40+264x^42+330x^43+648x^44+434x^45+2316x^46+1296x^47+378x^48+360x^49+114x^51+138x^52+22x^54+42x^55+2x^63

The gray image is a linear code over GF(3) with n=207, k=8 and d=120.
This code was found by Heurico 1.16 in 0.0817 seconds.