The generator matrix

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

generates a code of length 56 over Z2[X]/(X^3) who´s minimum homogenous weight is 53.

Homogenous weight enumerator: w(x)=1x^0+176x^53+312x^54+208x^55+56x^56+48x^58+80x^61+88x^62+48x^63+7x^64

The gray image is a linear code over GF(2) with n=224, k=10 and d=106.
This code was found by Heurico 1.16 in 51.7 seconds.