The generator matrix

 1  0  1  1  1  1  1 2X^2+X  1  1 2X  1  1  1  0  1 2X^2+X  1  1 2X  1  1  1  1 2X^2+X  0  1 2X  1  1  1 X^2  1  1  1  0  1 X^2  1
 0  1 2X^2+2X+1  2 2X^2+X X+1 2X^2+X+2  1 2X+2 2X  1 2X^2+1 2X^2+2X+1  2  1  0  1 2X^2+X 2X^2+X+2  1 2X X+1  0 2X+2  1  1  0  1 2X^2+X+2 2X+2 2X^2+1  1 2X+2 X^2+2X+2 X^2+2X+2  1 X+1  1 X^2
 0  0 2X^2  0  0  0 2X^2 2X^2 X^2 X^2 2X^2 2X^2 X^2 X^2 X^2 2X^2 X^2 2X^2 2X^2  0 X^2 2X^2 X^2 2X^2 X^2 X^2 X^2  0 X^2 2X^2  0 2X^2 X^2  0 X^2  0 2X^2  0 2X^2
 0  0  0 X^2  0 X^2 2X^2 X^2 X^2 2X^2  0 X^2 2X^2 X^2  0  0 2X^2 2X^2 2X^2  0 2X^2  0  0 X^2 X^2  0 X^2 X^2 X^2  0  0  0 2X^2 2X^2 2X^2 2X^2  0 2X^2 2X^2
 0  0  0  0 2X^2 2X^2 X^2  0 X^2 2X^2 2X^2 X^2 X^2 2X^2 X^2  0  0 X^2  0 2X^2  0 2X^2 2X^2 X^2 X^2  0 2X^2  0 X^2  0 2X^2 X^2 X^2 X^2 2X^2 X^2 X^2 2X^2 2X^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+90x^69+12x^70+156x^71+722x^72+90x^73+1074x^74+2172x^75+114x^76+3900x^77+3674x^78+132x^79+3786x^80+2848x^81+108x^82+276x^83+380x^84+30x^85+42x^86+40x^87+16x^90+4x^93+12x^96+4x^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 0.656 seconds.