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

generates a code of length 36 over Z3[X]/(X^3) who´s minimum homogenous weight is 67.

Homogenous weight enumerator: w(x)=1x^0+144x^67+432x^69+378x^70+72x^72+756x^73+180x^76+216x^78+8x^81

The gray image is a linear code over GF(3) with n=324, k=7 and d=201.
This code was found by Heurico 1.16 in 0.0299 seconds.