The generator matrix

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

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+390x^70+1212x^71+3806x^72+6402x^73+12036x^74+17460x^75+25878x^76+37524x^77+49858x^78+60216x^79+70926x^80+74054x^81+64272x^82+50184x^83+30274x^84+15732x^85+7332x^86+3062x^87+504x^88+96x^89+70x^90+102x^91+24x^92+20x^93+6x^94

The gray image is a linear code over GF(3) with n=360, k=12 and d=210.
This code was found by Heurico 1.16 in 293 seconds.