The generator matrix

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

generates a code of length 45 over Z3[X]/(X^3) who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+714x^84+282x^85+1614x^86+2444x^87+1590x^88+2118x^89+2678x^90+1638x^91+2016x^92+2148x^93+672x^94+876x^95+802x^96+18x^97+12x^98+30x^99+6x^100+6x^101+6x^103+12x^105

The gray image is a linear code over GF(3) with n=405, k=9 and d=252.
This code was found by Heurico 1.16 in 0.552 seconds.