The generator matrix

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

generates a code of length 57 over Z2[X]/(X^3) who´s minimum homogenous weight is 53.

Homogenous weight enumerator: w(x)=1x^0+110x^53+130x^54+176x^55+82x^56+176x^57+85x^58+72x^59+32x^60+38x^61+30x^62+40x^63+13x^64+20x^65+10x^66+8x^69+1x^74

The gray image is a linear code over GF(2) with n=228, k=10 and d=106.
This code was found by Heurico 1.11 in 0.062 seconds.