The generator matrix

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

generates a code of length 40 over Z3[X]/(X^3) who´s minimum homogenous weight is 71.

Homogenous weight enumerator: w(x)=1x^0+492x^71+1002x^72+1836x^73+4740x^74+5668x^75+8586x^76+13776x^77+14910x^78+19998x^79+25410x^80+23084x^81+21708x^82+18054x^83+9082x^84+4698x^85+2778x^86+822x^87+36x^88+324x^89+96x^90+30x^92+10x^93+6x^95

The gray image is a linear code over GF(3) with n=360, k=11 and d=213.
This code was found by Heurico 1.16 in 36.8 seconds.