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

generates a code of length 57 over Z2[X]/(X^3) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+155x^52+20x^53+132x^55+153x^56+216x^57+120x^59+126x^60+20x^61+4x^63+69x^64+6x^68+1x^72+1x^100

The gray image is a linear code over GF(2) with n=228, k=10 and d=104.
This code was found by Heurico 1.16 in 0.5 seconds.