The generator matrix

 1  0  1  1  1  1  1 2X^2+X  1  1  1 2X  1  1  1  0  1 2X^2+X  1  1  1  1  1  1
 0  1 2X^2+2X+1  2 2X^2+X X+1 2X^2+X+2  1 2X 2X^2+1 2X+2  1  0 2X^2+2X+1  2  1 2X^2+X  1 2X X+1 2X^2+X 2X^2+X 2X^2+2X+1  0
 0  0 2X^2  0  0  0 2X^2 2X^2  0 X^2 X^2 X^2  0  0 X^2 X^2 2X^2 X^2 2X^2  0  0  0 2X^2  0
 0  0  0 X^2  0  0 2X^2 2X^2 X^2 2X^2  0 2X^2 X^2 2X^2  0  0 X^2 X^2  0  0 X^2 X^2 2X^2  0
 0  0  0  0 2X^2  0 X^2 2X^2 X^2  0 2X^2 X^2 2X^2  0 2X^2 X^2  0  0 X^2 2X^2  0 X^2  0  0
 0  0  0  0  0 X^2 2X^2  0 2X^2 2X^2 2X^2 X^2 2X^2 X^2  0 2X^2 X^2 2X^2 X^2 2X^2 X^2 X^2 2X^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+50x^36+218x^39+54x^40+72x^41+1010x^42+648x^43+2682x^44+2616x^45+7452x^46+10152x^47+3820x^48+14040x^49+10242x^50+4088x^51+1134x^52+180x^53+422x^54+118x^57+32x^60+16x^63+2x^66

The gray image is a linear code over GF(3) with n=216, k=10 and d=108.
This code was found by Heurico 1.16 in 2.49 seconds.