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

generates a code of length 47 over Z3[X]/(X^3) who´s minimum homogenous weight is 85.

Homogenous weight enumerator: w(x)=1x^0+66x^85+86x^87+294x^88+440x^90+264x^91+486x^92+1512x^93+288x^94+972x^95+1484x^96+222x^97+78x^99+186x^100+12x^102+96x^103+8x^105+42x^106+10x^108+6x^111+6x^114+2x^126

The gray image is a linear code over GF(3) with n=423, k=8 and d=255.
This code was found by Heurico 1.16 in 0.21 seconds.