The generator matrix

 1  0  1  1  1  1  1 2X^2+X  1  1  1 2X  1  1  0  1  1  1  1 2X^2+X  1  1  1 2X  1  1  1  1  1  1 2X X^2+2X  1  1  1  1  1  1  1  1  1  1  1  0  1
 0  1 2X^2+2X+1  2 2X^2+X X+1 2X^2+X+2  1 2X 2X+2 2X^2+1  1 X+1 2X^2+X  1 2X^2+2X+1 2X^2+X+2  0 2X  1  2 2X^2+1 2X+2  1  0 2X 2X^2+2X+1 2X^2+1  2 X^2+2  1  1 X^2+2X X^2+2X+1 X^2 X^2+1 X^2+2X 2X+1 2X^2+X X^2 2X X^2 2X^2+X+2  1  0
 0  0 2X^2  0 2X^2 X^2 X^2 X^2  0  0 X^2  0 X^2 2X^2  0 2X^2 X^2  0 2X^2 X^2 X^2 2X^2  0 X^2 2X^2  0 X^2 2X^2  0 X^2  0 X^2  0 2X^2 2X^2 X^2 X^2  0 X^2  0 2X^2 X^2 2X^2 2X^2 X^2
 0  0  0 X^2 2X^2 2X^2 X^2  0 X^2 2X^2  0 2X^2 X^2  0 X^2 2X^2 2X^2 2X^2 X^2 X^2  0 X^2  0 2X^2 X^2  0  0  0  0 2X^2 X^2 X^2 2X^2 X^2 2X^2 2X^2  0  0 X^2 X^2  0 2X^2 2X^2  0 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+126x^84+366x^85+360x^86+620x^87+480x^88+798x^89+870x^90+828x^91+846x^92+610x^93+354x^94+90x^95+98x^96+78x^97+12x^98+16x^99+2x^102+4x^108+2x^114

The gray image is a linear code over GF(3) with n=405, k=8 and d=252.
This code was found by Heurico 1.16 in 0.105 seconds.