The generator matrix

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

generates a code of length 56 over Z2[X]/(X^3) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+91x^52+150x^53+185x^54+130x^55+109x^56+50x^57+88x^58+62x^59+45x^60+24x^61+30x^62+32x^63+20x^64+5x^68+1x^70+1x^76

The gray image is a linear code over GF(2) with n=224, k=10 and d=104.
This code was found by Heurico 1.11 in 0.079 seconds.