The generator matrix

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

generates a code of length 40 over Z3[X]/(X^3) who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+114x^70+108x^71+506x^72+774x^73+702x^74+1972x^75+4068x^76+2268x^77+5664x^78+11022x^79+3828x^80+7548x^81+11064x^82+2706x^83+3564x^84+1824x^85+504x^86+306x^87+222x^88+78x^89+102x^90+60x^91+12x^92+6x^93+12x^94+6x^96+4x^99+2x^102+2x^108

The gray image is a linear code over GF(3) with n=360, k=10 and d=210.
This code was found by Heurico 1.16 in 5.32 seconds.