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

generates a code of length 47 over Z3[X]/(X^3) who´s minimum homogenous weight is 81.

Homogenous weight enumerator: w(x)=1x^0+70x^81+42x^83+224x^84+144x^85+156x^86+336x^87+132x^88+168x^89+1512x^90+270x^91+1722x^92+4642x^93+288x^94+3258x^95+4704x^96+348x^97+264x^98+540x^99+216x^100+180x^101+162x^102+54x^103+42x^104+110x^105+6x^106+30x^108+28x^111+14x^114+14x^117+2x^120+2x^123+2x^126

The gray image is a linear code over GF(3) with n=423, k=9 and d=243.
This code was found by Heurico 1.16 in 1.52 seconds.