The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0  1  1  0  1  1  X  1  X  X  1  X  1  1  1
 0  X  0  0 2X 2X^2+X 2X^2+2X  X 2X X^2 2X 2X^2+X 2X^2+X  0 X^2 2X 2X^2+2X X^2+X  X  0 X^2  X  0 2X^2+2X  X X^2+X 2X^2+2X 2X^2 X^2 2X^2+2X 2X^2+X 2X  0 X^2+X  X 2X^2+X
 0  0  X 2X  0 X^2+2X X^2+X  X X^2+2X 2X^2 X^2+2X 2X^2+2X  0 X^2+X 2X^2+2X X^2 2X^2+X 2X X^2+X 2X X^2 X^2 X^2+X  0 2X^2+2X X^2+2X  X 2X 2X^2+X X^2+X 2X^2 X^2+2X 2X  0  X X^2+X
 0  0  0 X^2  0  0 2X^2  0  0 X^2 2X^2 2X^2 X^2 X^2  0 X^2 2X^2 2X^2 2X^2 2X^2  0 2X^2  0 2X^2  0 2X^2 X^2 2X^2 2X^2 2X^2  0 X^2 2X^2  0  0  0
 0  0  0  0 X^2 2X^2  0 X^2 2X^2  0 2X^2 2X^2  0  0  0 2X^2 X^2  0  0 X^2 X^2 X^2 2X^2 X^2 2X^2 X^2 2X^2 2X^2 2X^2 X^2  0 X^2 X^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+220x^63+150x^64+222x^65+604x^66+366x^67+756x^68+1394x^69+1746x^70+2226x^71+3466x^72+2838x^73+2262x^74+1660x^75+522x^76+234x^77+470x^78+180x^79+114x^80+150x^81+18x^82+18x^83+40x^84+12x^85+8x^87+6x^90

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 1.1 seconds.