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

generates a code of length 46 over Z3[X]/(X^3) who´s minimum homogenous weight is 85.

Homogenous weight enumerator: w(x)=1x^0+150x^85+180x^86+60x^87+372x^88+240x^89+868x^90+612x^91+1188x^92+1676x^93+564x^94+150x^95+40x^96+102x^97+120x^98+16x^99+36x^100+54x^101+8x^102+96x^103+12x^104+2x^105+12x^106+2x^129

The gray image is a linear code over GF(3) with n=414, k=8 and d=255.
This code was found by Heurico 1.16 in 0.305 seconds.