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.