The generator matrix

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

generates a code of length 24 over Z3[X]/(X^3) who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+34x^36+48x^37+90x^39+216x^40+162x^42+528x^43+486x^44+394x^45+2466x^46+1944x^47+5130x^48+4344x^49+1944x^50+546x^51+876x^52+102x^54+240x^55+48x^57+30x^58+30x^60+18x^63+6x^66

The gray image is a linear code over GF(3) with n=216, k=9 and d=108.
This code was found by Heurico 1.16 in 0.576 seconds.