The generator matrix

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

generates a code of length 35 over Z3[X]/(X^3) who´s minimum homogenous weight is 67.

Homogenous weight enumerator: w(x)=1x^0+474x^67+372x^68+10x^69+462x^70+270x^71+8x^72+462x^73+108x^74+4x^75+6x^76+6x^77+2x^78+2x^84

The gray image is a linear code over GF(3) with n=315, k=7 and d=201.
This code was found by Heurico 1.16 in 82.5 seconds.