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

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+84x^69+54x^71+226x^72+78x^74+274x^75+648x^76+120x^77+3102x^78+1296x^79+144x^80+160x^81+66x^83+110x^84+24x^86+104x^87+54x^90+12x^93+2x^96+2x^114

The gray image is a linear code over GF(3) with n=351, k=8 and d=207.
This code was found by Heurico 1.16 in 0.157 seconds.