The generator matrix

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

generates a code of length 24 over Z3[X]/(X^3) who´s minimum homogenous weight is 43.

Homogenous weight enumerator: w(x)=1x^0+78x^43+264x^44+804x^45+870x^46+624x^47+926x^48+1284x^49+672x^50+756x^51+180x^52+48x^53+8x^54+18x^55+12x^56+16x^57

The gray image is a linear code over GF(3) with n=216, k=8 and d=129.
This code was found by Heurico 1.16 in 0.0407 seconds.