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

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+122x^69+240x^70+228x^71+654x^72+660x^73+696x^74+1686x^75+1554x^76+1482x^77+4288x^78+2322x^79+1536x^80+2294x^81+612x^82+252x^83+264x^84+300x^85+156x^86+124x^87+138x^88+18x^89+30x^90+6x^91+6x^92+12x^93+2x^96

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 1.07 seconds.