The generator matrix

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

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+832x^72+504x^73+594x^74+3270x^75+2862x^76+2916x^77+6822x^78+6696x^79+5670x^80+10710x^81+7596x^82+3780x^83+4140x^84+1296x^85+162x^86+894x^87+256x^90+42x^93+6x^96

The gray image is a linear code over GF(3) with n=360, k=10 and d=216.
This code was found by Heurico 1.16 in 54.2 seconds.