The generator matrix

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

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+144x^40+120x^41+406x^42+480x^43+576x^44+526x^45+2568x^46+1722x^47+4646x^48+4752x^49+1680x^50+672x^51+582x^52+234x^53+254x^54+204x^55+42x^56+52x^57+18x^58+2x^60+2x^63

The gray image is a linear code over GF(3) with n=216, k=9 and d=120.
This code was found by Heurico 1.16 in 0.579 seconds.