The generator matrix

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

generates a code of length 24 over Z3[X]/(X^3) who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+66x^40+142x^42+168x^43+132x^45+798x^46+3096x^48+1602x^49+180x^51+210x^52+68x^54+66x^55+6x^58+18x^60+6x^63+2x^69

The gray image is a linear code over GF(3) with n=216, k=8 and d=120.
This code was found by Heurico 1.16 in 0.0797 seconds.