The generator matrix

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

generates a code of length 24 over Z3[X]/(X^2) who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+168x^40+186x^41+264x^42+324x^43+504x^44+392x^45+558x^46+594x^47+412x^48+666x^49+678x^50+378x^51+558x^52+396x^53+204x^54+126x^55+72x^56+50x^57+30x^58

The gray image is a linear code over GF(3) with n=72, k=8 and d=40.
This code was found by Heurico 1.16 in 0.207 seconds.