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 X^3  X X^2  X  X  0  X X^3+X^2  X  X X^2  X  0  1  1  1  1  1  1  1  1
 0  X  0 X^3+X^2+X  0 X^2+X  0 X^3+X X^2 X^2+X X^3+X^2  X X^2 X^3+X^2+X X^3+X^2 X^3+X X^3 X^2+X X^3  X X^3 X^3+X^2+X X^3 X^3+X X^3+X^2 X^3+X^2+X X^2 X^3+X X^3+X^2 X^2+X X^2  X X^2+X  X X^3+X  X X^3 X^3+X^2+X  X  X  X  0 X^2 X^3 X^3+X^2  0  0 X^2 X^3 X^3+X^2 X^2+X X^3+X^2+X X^3+X  X
 0  0 X^3+X^2 X^2 X^3 X^3+X^2 X^2 X^3 X^2  0  0 X^2 X^3+X^2 X^3 X^3 X^3+X^2 X^3 X^3 X^2 X^3+X^2  0  0 X^3+X^2 X^2 X^3+X^2 X^3+X^2 X^3  0 X^2 X^2  0 X^3  0 X^2 X^3 X^3+X^2 X^2 X^2 X^3 X^2  0 X^2 X^2 X^3+X^2 X^3+X^2 X^2  0 X^3+X^2 X^3 X^2  0 X^3  0 X^3

generates a code of length 54 over Z2[X]/(X^4) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+90x^52+192x^53+96x^54+52x^56+64x^57+14x^60+2x^64+1x^80

The gray image is a linear code over GF(2) with n=432, k=9 and d=208.
This code was found by Heurico 1.16 in 0.125 seconds.