The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  X  1  1
 0 X^2  0  0  0  0  0 X^2 X^2  0  0 2X^2 X^2 X^2 X^2 X^2 2X^2 X^2 2X^2 X^2  0  0  0  0
 0  0 X^2  0  0  0 X^2 2X^2 2X^2  0 2X^2 X^2 X^2 X^2 X^2 2X^2 2X^2  0  0 2X^2 X^2  0 X^2  0
 0  0  0 X^2  0  0 2X^2 2X^2 X^2 X^2  0 X^2  0 X^2  0 2X^2 X^2  0 X^2  0 2X^2 X^2  0  0
 0  0  0  0 X^2  0 2X^2 X^2 2X^2 X^2 2X^2  0 X^2 X^2  0 X^2 2X^2 2X^2  0  0  0 X^2  0  0
 0  0  0  0  0 X^2 X^2  0 X^2 X^2 2X^2 2X^2 2X^2 X^2 X^2 X^2 X^2 2X^2 2X^2  0 2X^2 2X^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+30x^36+86x^39+120x^42+162x^44+84x^45+648x^47+4476x^48+648x^50+102x^51+68x^54+78x^57+48x^60+6x^63+4x^66

The gray image is a linear code over GF(3) with n=216, k=8 and d=108.
This code was found by Heurico 1.16 in 0.0967 seconds.