The generator matrix

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

generates a code of length 23 over Z3[X]/(X^3) who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+68x^36+114x^39+108x^42+486x^44+102x^45+4374x^46+972x^47+92x^48+108x^51+86x^54+26x^57+18x^60+4x^63+2x^66

The gray image is a linear code over GF(3) with n=207, k=8 and d=108.
This code was found by Heurico 1.16 in 0.0951 seconds.