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

generates a code of length 36 over Z3[X]/(X^3) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+162x^68+108x^69+288x^70+318x^71+552x^72+324x^73+270x^74+30x^75+36x^77+24x^78+36x^79+6x^80+12x^81+18x^83+2x^99

The gray image is a linear code over GF(3) with n=324, k=7 and d=204.
This code was found by Heurico 1.16 in 18.5 seconds.