The generator matrix

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

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+34x^52+130x^53+102x^54+128x^55+93x^56+190x^57+47x^58+72x^59+46x^60+78x^61+34x^62+20x^63+13x^64+18x^65+5x^66+2x^68+2x^70+4x^71+2x^72+2x^74+1x^80

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 0.139 seconds.