The generator matrix
1 0 1 1 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 1 0 1 1 1 1 0 1 1 1 1 1 1 X 1 1 1 1 1 1 1
0 1 1 2 0 1 2 1 0 2X+1 2 1 2X+1 0 2 1 X+1 X X+2 0 1 2 2 0 X 1 0 2X+1 2X+1 2X+1 X+2 2X+1 1 X 1 X 0 2X+1 0 0
0 0 2X 0 0 0 0 0 0 0 0 0 0 X X 2X X X 2X X X X X X X 2X 0 2X 2X 2X 2X 0 0 X 0 X 2X 2X 0 0
0 0 0 X 0 0 0 0 X 2X X 2X X 2X 2X 0 0 0 2X 0 X 2X 2X X 2X 0 2X X 2X X X X X 2X 2X 2X 0 X 0 0
0 0 0 0 X 0 0 X 2X 2X X X 0 2X 2X 2X X 2X 2X 2X 0 X X X X 0 X 0 0 0 0 2X 2X X X X 2X 0 0 X
0 0 0 0 0 2X 0 2X X 0 X X 2X 2X X 2X 0 0 0 X X X X 0 2X 2X 2X X 0 0 0 X X 0 0 0 2X X X 2X
0 0 0 0 0 0 X 2X 0 2X 2X X X 2X 2X X 0 2X X X X 2X 0 2X X 2X X X 2X 0 X 2X 0 X 2X 0 0 0 0 2X
generates a code of length 40 over Z3[X]/(X^2) who´s minimum homogenous weight is 63.
Homogenous weight enumerator: w(x)=1x^0+42x^63+18x^64+102x^66+78x^67+248x^69+408x^70+378x^72+1188x^73+806x^75+2106x^76+1408x^78+2982x^79+1532x^81+3294x^82+1170x^84+2124x^85+474x^87+768x^88+150x^90+144x^91+126x^93+12x^94+82x^96+30x^99+10x^102+2x^105
The gray image is a linear code over GF(3) with n=120, k=9 and d=63.
This code was found by Heurico 1.16 in 3.43 seconds.