The generator matrix

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

generates a code of length 45 over Z3[X]/(X^3) who´s minimum homogenous weight is 83.

Homogenous weight enumerator: w(x)=1x^0+354x^83+336x^84+1026x^85+1272x^86+810x^87+1908x^88+3252x^89+1268x^90+2862x^91+3204x^92+992x^93+1458x^94+450x^95+216x^96+36x^97+96x^98+16x^99+96x^101+2x^102+24x^104+2x^111+2x^117

The gray image is a linear code over GF(3) with n=405, k=9 and d=249.
This code was found by Heurico 1.16 in 0.742 seconds.