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

generates a code of length 47 over Z3[X]/(X^3) who�s minimum homogenous weight is 90.

Homogenous weight enumerator: w(x)=1x^0+222x^90+216x^93+1458x^94+216x^96+36x^99+36x^108+2x^135

The gray image is a linear code over GF(3) with n=423, k=7 and d=270.
This code was found by Heurico 1.16 in 22 seconds.