The generator matrix

 1  0  1  1  1  1  1 2X^2+X  1  1 2X  1  1  1  0  1 2X^2+X  1  1  1  1  1  1 2X  1  0  1  1  1 2X^2+X  1  1  1  1  1  1  1 2X^2+X  0  1
 0  1 2X^2+2X+1  2 2X^2+X X+1 2X^2+X+2  1 2X+2 2X  1 2X^2+1 2X^2+2X+1  2  1 2X^2+1  1 2X^2+X+2 2X+2 X+1  0 2X 2X^2+X  1  2  1 2X^2+2X+1 2X+2 2X^2+1  1 2X^2+X 2X^2+1 2X^2+2X+1 X+1 2X^2+X 2X+2 X^2+2X+1  1  X  0
 0  0 2X^2  0  0  0 2X^2 2X^2 X^2 X^2 2X^2 2X^2 X^2 X^2 X^2  0 X^2 2X^2  0  0  0 2X^2 2X^2 X^2  0 X^2 2X^2 2X^2 2X^2 2X^2  0  0  0  0 X^2 2X^2 2X^2 2X^2 X^2 2X^2
 0  0  0 X^2  0 X^2 2X^2 X^2 X^2 2X^2  0 X^2 2X^2 X^2  0  0 2X^2 2X^2 2X^2  0 X^2  0  0 X^2 X^2 2X^2  0 2X^2 2X^2  0 2X^2 X^2  0 X^2 X^2  0 2X^2  0 2X^2 X^2
 0  0  0  0 2X^2 2X^2 X^2  0 X^2 2X^2 2X^2 X^2 X^2 2X^2 X^2 X^2  0  0 2X^2  0 2X^2 X^2  0  0 X^2 X^2 2X^2 2X^2 X^2 X^2 X^2  0  0 X^2  0 X^2 2X^2  0 2X^2 2X^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+282x^72+162x^73+162x^74+976x^75+756x^76+1458x^77+2094x^78+2268x^79+2430x^80+2854x^81+2268x^82+1782x^83+1494x^84+378x^85+258x^87+38x^90+10x^93+4x^96+4x^102+2x^105+2x^108

The gray image is a linear code over GF(3) with n=360, k=9 and d=216.
This code was found by Heurico 1.16 in 1.27 seconds.