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

generates a code of length 40 over Z3[X]/(X^3) who´s minimum homogenous weight is 69.

Homogenous weight enumerator: w(x)=1x^0+84x^69+106x^72+102x^75+162x^76+104x^78+648x^79+4374x^80+76x^81+648x^82+70x^84+52x^87+50x^90+40x^93+24x^96+10x^99+4x^102+4x^105+2x^114

The gray image is a linear code over GF(3) with n=360, k=8 and d=207.
This code was found by Heurico 1.16 in 0.22 seconds.