The generator matrix

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

generates a code of length 23 over Z3[X]/(X^2) who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+132x^40+174x^41+80x^42+252x^43+330x^44+66x^45+228x^46+180x^47+48x^48+210x^49+222x^50+26x^51+144x^52+66x^53+14x^54+6x^55+6x^57+2x^60

The gray image is a linear code over GF(3) with n=69, k=7 and d=40.
This code was found by Heurico 1.13 in 0.0137 seconds.