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

generates a code of length 40 over Z3[X]/(X^3) who´s minimum homogenous weight is 73.

Homogenous weight enumerator: w(x)=1x^0+126x^73+180x^74+66x^75+246x^76+354x^77+1052x^78+204x^79+1434x^80+1962x^81+162x^82+294x^83+16x^84+90x^85+96x^86+58x^87+102x^88+60x^89+2x^90+36x^91+12x^92+6x^94+2x^111

The gray image is a linear code over GF(3) with n=360, k=8 and d=219.
This code was found by Heurico 1.16 in 0.149 seconds.