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  X  1  1  1  1  X  1  0  1  1  1  1  1  1  1  1  1  X
 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 X^2 2X^2+2X 2X^2+X X^2 2X 2X^2+2X 2X^2+X 2X^2+X 2X^2+X  0 2X 2X X^2+2X  X  0 2X^2+X  X  0 2X^2 X^2+X 2X^2 2X^2 X^2+X 2X^2+X
 0  0 X^2  0  0  0  0 2X^2 X^2  0 X^2 2X^2 X^2  0 2X^2 2X^2 2X^2  0 X^2 2X^2 2X^2  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0 X^2 2X^2  0  0  0 2X^2 2X^2 2X^2  0
 0  0  0 X^2  0  0  0  0  0 2X^2 X^2 2X^2 2X^2 2X^2 X^2 2X^2 2X^2 2X^2 2X^2 X^2  0  0 2X^2 X^2 X^2  0 2X^2  0 2X^2 X^2 X^2  0 X^2 X^2  0 2X^2  0 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  0  0 X^2 2X^2 2X^2 2X^2 2X^2  0 2X^2  0  0 2X^2 2X^2  0 X^2 2X^2 2X^2  0  0  0 X^2 X^2  0 2X^2
 0  0  0  0  0 X^2 X^2  0 2X^2 X^2 X^2 X^2 2X^2  0 2X^2 2X^2 2X^2 2X^2 2X^2 X^2 2X^2 X^2 2X^2 2X^2 2X^2 2X^2  0  0 X^2 X^2 2X^2 X^2  0 2X^2 2X^2 X^2 2X^2 X^2 2X^2 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+162x^69+588x^72+792x^75+486x^76+4302x^78+1944x^79+7388x^81+1944x^82+1322x^84+536x^87+140x^90+32x^93+20x^96+8x^99+14x^102+2x^105+2x^108

The gray image is a linear code over GF(3) with n=360, k=9 and d=207.
This code was found by Heurico 1.16 in 2.39 seconds.