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  X  1  1  1  1  1  X  1  1  0  1  1  1  X  1  1  1  1  X X^2  1
 0  X 2X  0 2X^2+X 2X  0 2X^2+X 2X X^2 2X^2+X 2X X^2+X X^2+2X  0 X^2+X X^2 2X^2+2X 2X^2+X X^2 2X 2X^2+2X 2X^2+X 2X^2+X 2X^2+X  0 2X X^2+2X 2X 2X^2 2X^2+X  X X^2+2X  X  0 2X^2+X 2X 2X^2  X 2X^2 2X X^2 2X^2+X
 0  0 X^2  0  0  0  0 2X^2 X^2  0 X^2 2X^2 X^2  0 2X^2 2X^2 2X^2  0 X^2 2X^2 2X^2  0  0 X^2 X^2 X^2 X^2 X^2 2X^2 X^2 2X^2 X^2 X^2  0  0 2X^2  0  0 X^2 X^2 2X^2  0  0
 0  0  0 X^2  0  0  0  0  0 2X^2 X^2 2X^2 2X^2 2X^2 X^2 2X^2 2X^2 2X^2 2X^2 X^2  0  0 2X^2 X^2 X^2  0 2X^2 2X^2 2X^2 2X^2 X^2  0 2X^2 X^2 X^2 X^2 X^2 X^2 2X^2 2X^2 2X^2 X^2 X^2
 0  0  0  0 2X^2  0 X^2 2X^2 X^2 X^2 2X^2 2X^2 2X^2 2X^2  0  0  0  0 X^2 2X^2 2X^2 2X^2 2X^2  0 2X^2  0  0 2X^2  0 X^2 2X^2 X^2 2X^2 X^2  0 2X^2  0 2X^2  0  0 X^2  0 X^2
 0  0  0  0  0 X^2 X^2  0 2X^2 X^2 X^2 X^2 2X^2  0 2X^2 2X^2 2X^2 2X^2 2X^2 X^2 2X^2 X^2 2X^2 2X^2 2X^2 2X^2  0 X^2 2X^2  0  0  0  0  0 2X^2 2X^2 X^2 X^2 X^2  0 X^2 X^2 2X^2

generates a code of length 43 over Z3[X]/(X^3) who´s minimum homogenous weight is 75.

Homogenous weight enumerator: w(x)=1x^0+172x^75+96x^76+30x^77+412x^78+156x^79+444x^80+490x^81+708x^82+2244x^83+598x^84+2244x^85+4398x^86+680x^87+2196x^88+2958x^89+690x^90+264x^91+132x^92+376x^93+144x^94+134x^96+24x^97+30x^99+36x^102+16x^105+4x^108+6x^111

The gray image is a linear code over GF(3) with n=387, k=9 and d=225.
This code was found by Heurico 1.16 in 81 seconds.