The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  X  X  1  X  X  1  1  X  X  1  1
 0  X  0  0  0  0  0  0  0  0  0  0  0  0 2X  X 2X  X 2X  0  X 2X 2X  X 2X 2X  0 2X  X  X  0  X  X  X 2X  0  X  X 2X  X  X  X  0
 0  0  X  0  0  0  0  0  0  0  0  X  X  X  0 2X 2X 2X 2X  X  0  X  0 2X  X  X 2X  0  0  0 2X  X  0  0 2X  X  X  0 2X 2X  X 2X  0
 0  0  0  X  0  0  0  0  0  X  X 2X 2X 2X  0 2X 2X 2X 2X  X  X 2X 2X  X 2X  X  X 2X 2X  0 2X 2X 2X  0 2X  0 2X  X 2X  0  X  0  0
 0  0  0  0  X  0  0  0  X 2X 2X 2X  X  X  0 2X 2X  X  X  0  0 2X 2X  0 2X  X  0  0  0 2X  X  0  X  X  0  0  X 2X  X  X 2X  0  X
 0  0  0  0  0  X  0  0 2X 2X  X  X  0 2X 2X 2X 2X  X 2X 2X  0  0  0  0 2X  0  0  0  X  0  X  X  0  X  X  X 2X 2X  0  0 2X 2X 2X
 0  0  0  0  0  0  X  0 2X  X 2X  X 2X  0 2X  0 2X 2X  X 2X  X  X 2X  0  0  X 2X  X  X 2X  0 2X 2X 2X  0 2X 2X  0  0 2X  X 2X 2X
 0  0  0  0  0  0  0  X  X  0  X  0  X  0 2X 2X  0  X  X 2X  X  X  0  X  X 2X  X  0 2X  X 2X  X  0  0  0  0 2X  0  X 2X  X  0  0

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+68x^66+234x^69+372x^72+570x^75+1056x^78+2316x^81+4074x^84+4920x^87+3352x^90+1448x^93+550x^96+364x^99+208x^102+94x^105+48x^108+4x^111+4x^114

The gray image is a linear code over GF(3) with n=129, k=9 and d=66.
This code was found by Heurico 1.16 in 6.53 seconds.