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

generates a code of length 40 over Z3[X]/(X^3) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+88x^72+150x^73+146x^75+258x^76+1104x^78+426x^79+1458x^80+2070x^81+348x^82+114x^84+156x^85+56x^87+96x^88+44x^90+24x^91+10x^93+8x^96+2x^99+2x^114

The gray image is a linear code over GF(3) with n=360, k=8 and d=216.
This code was found by Heurico 1.16 in 0.164 seconds.