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

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+86x^63+78x^65+220x^66+78x^68+186x^69+648x^70+102x^71+3168x^72+1296x^73+114x^74+208x^75+66x^77+166x^78+42x^80+44x^81+6x^83+40x^84+6x^87+4x^90+2x^105

The gray image is a linear code over GF(3) with n=324, k=8 and d=189.
This code was found by Heurico 1.16 in 0.14 seconds.