The generator matrix

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

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+48x^40+60x^41+64x^42+114x^43+120x^44+64x^45+264x^46+360x^47+36x^48+300x^49+300x^50+24x^51+192x^52+132x^53+8x^54+42x^55+32x^57+12x^58+2x^60+8x^63+4x^66

The gray image is a linear code over GF(3) with n=72, k=7 and d=40.
This code was found by Heurico 1.16 in 0.0385 seconds.