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  X  X  X  1  1  X  1  X  1
 0 X^2  0  0  0  0  0  0  0  0 X^2 2X^2 2X^2 X^2 X^2 X^2  0 2X^2 2X^2 X^2 X^2 X^2 2X^2  0  0 X^2 X^2 X^2 X^2 2X^2  0 X^2 2X^2  0  0 X^2  0 X^2 X^2  0 X^2 2X^2  0 X^2  0 X^2  0
 0  0 X^2  0  0  0  0 X^2 2X^2 2X^2 2X^2  0  0 2X^2 X^2 2X^2 X^2  0 X^2 X^2 X^2  0  0 2X^2 2X^2  0 2X^2 X^2 2X^2 2X^2  0 X^2 X^2 X^2  0 X^2 X^2 X^2  0  0 2X^2  0  0 X^2  0 2X^2  0
 0  0  0 X^2  0  0 X^2 2X^2  0 2X^2  0  0 2X^2 X^2 X^2 2X^2  0 X^2 2X^2 2X^2 2X^2 X^2  0 2X^2 2X^2 2X^2 2X^2  0 2X^2  0 X^2 2X^2 X^2 2X^2 2X^2 X^2 2X^2 X^2 X^2  0 X^2 2X^2  0 2X^2 2X^2 2X^2  0
 0  0  0  0 X^2  0 2X^2 2X^2 X^2  0 2X^2 2X^2 2X^2  0 2X^2 2X^2  0 2X^2 2X^2 X^2  0  0  0 2X^2 2X^2  0 X^2  0 2X^2 2X^2 2X^2 2X^2  0 X^2 2X^2  0 X^2  0 X^2 X^2 X^2  0 2X^2 X^2 X^2 X^2  0
 0  0  0  0  0 X^2 2X^2 2X^2 2X^2 2X^2 2X^2 2X^2 X^2 2X^2 X^2 X^2 2X^2 X^2  0 2X^2 2X^2  0 X^2 2X^2 X^2 X^2 X^2 X^2 2X^2  0  0 2X^2  0 X^2 X^2 X^2 2X^2 2X^2  0 2X^2 2X^2 X^2 X^2  0  0 X^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+46x^81+100x^84+142x^87+328x^90+658x^93+4374x^94+474x^96+270x^99+32x^102+56x^105+24x^108+16x^111+28x^114+4x^117+4x^120+2x^123+2x^126

The gray image is a linear code over GF(3) with n=423, k=8 and d=243.
This code was found by Heurico 1.16 in 0.273 seconds.