The generator matrix

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

generates a code of length 36 over Z3[X]/(X^3) who´s minimum homogenous weight is 69.

Homogenous weight enumerator: w(x)=1x^0+68x^69+180x^70+108x^72+288x^73+48x^75+18x^76+16x^78+2x^90

The gray image is a linear code over GF(3) with n=324, k=6 and d=207.
This code was found by Heurico 1.16 in 0.0146 seconds.