The generator matrix

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

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+120x^40+198x^41+82x^42+246x^43+288x^44+74x^45+264x^46+216x^47+14x^48+204x^49+180x^50+60x^51+132x^52+90x^53+6x^54+6x^55+4x^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 1.16 in 0.0298 seconds.