The generator matrix

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

generates a code of length 36 over Z3[X]/(X^3) who´s minimum homogenous weight is 63.

Homogenous weight enumerator: w(x)=1x^0+28x^63+60x^64+198x^65+480x^66+222x^67+1074x^68+1896x^69+1020x^70+2922x^71+3490x^72+1644x^73+3114x^74+2366x^75+408x^76+456x^77+190x^78+42x^79+12x^80+28x^81+6x^82+12x^84+2x^87+8x^90+4x^93

The gray image is a linear code over GF(3) with n=324, k=9 and d=189.
This code was found by Heurico 1.16 in 0.592 seconds.