The generator matrix
1 0 1 1 1 1 1 0 1 1 1 0 1 1 1 0 X 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 2X 1 1 1 1 1 1 1 1 1 1
0 1 1 2 0 1 2 1 0 2X+1 2 1 0 2 2X+1 1 1 X+2 0 2X+1 1 2 2X+1 0 2 2 0 2X+1 X+1 2 X 1 1 1 1 X+2 X X 2X+1 0 X 2 0
0 0 2X 0 0 0 0 0 0 2X X 2X 2X 2X 2X 0 2X 0 2X 2X X 0 2X 2X 2X X 0 2X 0 X 2X X 2X 2X 0 X X 0 0 X X X 0
0 0 0 X 0 0 0 0 0 0 0 0 0 0 2X X 2X X 0 X 0 X 2X 2X 0 2X 2X X 0 2X 2X X X X 0 2X X 2X 0 0 X 2X X
0 0 0 0 X 0 0 0 0 0 0 0 0 0 2X 2X X 0 2X X 2X 2X 0 2X X 0 2X 2X 2X 2X 0 2X 0 X 2X X X 0 2X X 2X 0 2X
0 0 0 0 0 2X 0 0 X 2X 2X X 2X 0 2X 2X 2X X 0 0 X 0 X 2X 0 2X 0 0 X 0 2X 2X 2X X X 0 2X X 0 0 X 0 2X
0 0 0 0 0 0 X 0 X 0 X X X 2X 2X 0 X 2X 2X 0 2X 0 X 0 X X X 2X 0 X X 0 2X X X 2X 0 0 X 0 0 0 2X
0 0 0 0 0 0 0 X X X X 0 2X X 2X X X X X 2X X 2X 2X X X 0 2X 0 X 2X 0 X X 2X 2X 2X 0 2X 2X 2X 2X 0 X
generates a code of length 43 over Z3[X]/(X^2) who´s minimum homogenous weight is 66.
Homogenous weight enumerator: w(x)=1x^0+70x^66+240x^69+24x^70+438x^72+216x^73+910x^75+1176x^76+1550x^78+2910x^79+2258x^81+6390x^82+3302x^84+10410x^85+4040x^87+9408x^88+3164x^90+6354x^91+1942x^93+2184x^94+984x^96+294x^97+452x^99+184x^102+96x^105+32x^108+18x^111+2x^123
The gray image is a linear code over GF(3) with n=129, k=10 and d=66.
This code was found by Heurico 1.16 in 30.9 seconds.