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

generates a code of length 35 over Z3[X]/(X^3) who´s minimum homogenous weight is 63.

Homogenous weight enumerator: w(x)=1x^0+254x^63+582x^66+1206x^69+2916x^70+1138x^72+276x^75+144x^78+32x^81+6x^84+4x^90+2x^99

The gray image is a linear code over GF(3) with n=315, k=8 and d=189.
This code was found by Heurico 1.16 in 0.919 seconds.