The generator matrix

 1  0  1  1  1  1  1 2X^2+X  1  1  1 2X  1  1  0  1  1  1  1  1  1 2X^2+X  1  1 2X  1  1  1  1  1  1  1  1  0 2X  1
 0  1 2X^2+2X+1  2 2X^2+X X+1 2X^2+X+2  1 2X 2X+2 2X^2+1  1 X+1 2X^2+X  1  2 2X^2+X+2 2X+2  0 2X 2X^2+2X+1  1  2 2X^2+1  1 X^2+2 X^2+2 2X^2+X+2 X^2+X+2  0 2X 2X^2+1 X+1  1  1 X^2
 0  0 2X^2  0 2X^2 X^2 X^2 X^2  0  0 X^2  0 X^2 2X^2  0 2X^2 X^2 X^2  0 2X^2 2X^2 X^2  0 2X^2 X^2 X^2  0  0 2X^2 X^2 2X^2 2X^2  0 2X^2 X^2 2X^2
 0  0  0 X^2 2X^2 2X^2 X^2  0 X^2 2X^2  0 2X^2 X^2  0 X^2 2X^2  0 2X^2 2X^2 X^2 2X^2 X^2  0 X^2 2X^2 2X^2 2X^2 X^2  0 X^2  0 2X^2 2X^2 2X^2 X^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+124x^66+126x^67+528x^68+596x^69+270x^70+1092x^71+1148x^72+378x^73+1134x^74+770x^75+198x^76+120x^77+16x^78+42x^80+12x^81+4x^84+2x^93

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 0.0742 seconds.