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

generates a code of length 46 over Z3[X]/(X^3) who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+88x^84+186x^85+134x^87+414x^88+142x^90+1050x^91+2916x^92+150x^93+1002x^94+84x^96+114x^97+72x^99+84x^100+32x^102+54x^103+12x^105+12x^106+10x^108+2x^114+2x^132

The gray image is a linear code over GF(3) with n=414, k=8 and d=252.
This code was found by Heurico 1.16 in 0.204 seconds.