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

generates a code of length 36 over Z3[X]/(X^3) who´s minimum homogenous weight is 66.

Homogenous weight enumerator: w(x)=1x^0+384x^66+162x^68+564x^69+486x^70+648x^71+1966x^72+972x^73+648x^74+324x^75+210x^78+182x^81+12x^84+2x^99

The gray image is a linear code over GF(3) with n=324, k=8 and d=198.
This code was found by Heurico 1.16 in 0.273 seconds.