The generator matrix
1 0 1 1 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 1 1 X 1 X 1 1 1 1 0 1 1 1 1 1 0 1 1 2X X 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 1 X+2 0 1 2 1 X 2X+1 X+1 2 1 X+2 2X+1 1 0 2X 1 X+2 1 1 1 2X+1 0 0
0 0 2X 0 0 0 0 0 0 0 0 0 0 X X 2X X X 2X 2X X X X X X 2X 0 2X 0 X X 2X 2X 2X 2X X 0 X X 0 2X 0 0
0 0 0 X 0 0 0 0 X 2X X 2X X 2X 2X 0 0 0 2X X 0 2X 2X 2X X 0 0 2X 0 2X 2X 2X 2X 0 0 2X 2X 2X 0 2X 2X X 0
0 0 0 0 X 0 0 X 2X 2X X X 0 2X 2X 2X X 2X 2X 0 2X 2X X 0 2X 0 0 0 2X 2X X 0 2X 0 X 2X 0 X X X 2X 0 0
0 0 0 0 0 2X 0 2X X 0 X X 2X 2X X 2X 0 0 0 0 X X X X X X X X 0 0 X 2X 0 X 2X 0 X 0 2X 0 X 0 0
0 0 0 0 0 0 X 2X 0 2X 2X X X 2X 2X X 0 2X X 0 X 0 0 X 2X 0 2X 0 0 X 2X 0 2X 2X 0 0 X 2X 0 X 0 X 0
generates a code of length 43 over Z3[X]/(X^2) who´s minimum homogenous weight is 69.
Homogenous weight enumerator: w(x)=1x^0+52x^69+152x^72+120x^73+276x^75+552x^76+508x^78+1116x^79+834x^81+1920x^82+1132x^84+3072x^85+1386x^87+3258x^88+1126x^90+2064x^91+560x^93+804x^94+278x^96+216x^97+110x^99+80x^102+44x^105+18x^108+4x^111
The gray image is a linear code over GF(3) with n=129, k=9 and d=69.
This code was found by Heurico 1.16 in 3.83 seconds.