The generator matrix

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

generates a code of length 39 over Z3[X]/(X^3) who´s minimum homogenous weight is 66.

Homogenous weight enumerator: w(x)=1x^0+66x^66+108x^68+200x^69+366x^71+296x^72+1728x^74+340x^75+1458x^76+4896x^77+370x^78+2916x^79+5118x^80+414x^81+702x^83+296x^84+180x^86+94x^87+24x^89+52x^90+32x^93+20x^96+2x^99+4x^102

The gray image is a linear code over GF(3) with n=351, k=9 and d=198.
This code was found by Heurico 1.16 in 1.2 seconds.