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

generates a code of length 39 over Z3[X]/(X^3) who´s minimum homogenous weight is 69.

Homogenous weight enumerator: w(x)=1x^0+328x^69+1236x^72+648x^74+2218x^75+486x^76+2592x^77+4800x^78+972x^79+2592x^80+2516x^81+850x^84+324x^87+102x^90+10x^93+2x^96+6x^99

The gray image is a linear code over GF(3) with n=351, k=9 and d=207.
This code was found by Heurico 1.16 in 1.12 seconds.