The generator matrix

 1  0  1  1  1 X^3+X^2+X  1  1  X  1  1 X^3+X^2  1  1 X^3  1  1 X^2+X  1  1 X^2  1  1 X^3+X  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0  1  1  1  X  1  1  0 X^3+X^2 X^3+X X^2+X
 0  1 X+1 X^3+X^2+X X^2+1  1  X X^2+X+1  1 X^3+X^2 X^3+1  1 X^3 X+1  1 X^2+X X^3+X^2+1  1 X^3+X X^3+X^2+X+1  1 X^2  1  1  0 X^3+X^2+X X^3+X^2  X X+1 X^3+X^2+1 X^3+X^2+X+1  1  0 X^3+X^2+X X^3+X^2  X X^3+X+1 X^3+X^2+1 X^3+X^2+X+1  1 X^3 X^3 X^3  1 X^2+X X^2+X X^3+X X^2 X^2 X^2  1  X  1  1
 0  0 X^2 X^3+X^2 X^3 X^2 X^2 X^3+X^2 X^3+X^2 X^3  0 X^3 X^2  0 X^2  0 X^2  0 X^3 X^3 X^3+X^2 X^3+X^2 X^3+X^2 X^3 X^3 X^2  0 X^3+X^2 X^3 X^3+X^2  0 X^2 X^3+X^2 X^3 X^2  0 X^3+X^2  0 X^2 X^3 X^3  0 X^3+X^2 X^3 X^2 X^3+X^2  0 X^2 X^3 X^2 X^3+X^2 X^2 X^2 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+324x^52+120x^53+208x^54+48x^55+265x^56+24x^57+32x^58+1x^72+1x^80

The gray image is a linear code over GF(2) with n=432, k=10 and d=208.
This code was found by Heurico 1.16 in 0.578 seconds.