The generator matrix

 1  0  1  1  1 X^2+X  1  1  0  1  1 X^2+X  1  1  0  1  1 X^2+X  1  1 X^2  1  1  X  1  1  0  1  1 X^2+X  1  1  0  1  1 X^2+X  1  1  1  1  1  1  1  1  1  1  1  1  1 X^2  1  1  0  1  1  1
 0  1 X+1 X^2+X  1  1 X+1  0  1 X^2+X X^2+1  1  0 X+1  1 X^2+X X^2+1  1 X^2 X^2+X+1  1  X X^2+1  1  0 X+1  1 X^2+X X^2+1  1  0 X+1  1 X^2+X X^2+1  1  0 X^2+X X^2  X  0 X^2+X X^2  X X^2  X X^2  X  X  0 X^2+X X+1  1 X^2 X^2  0
 0  0 X^2  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2  0  0 X^2 X^2  0  0 X^2  0  0 X^2  0  0 X^2  0
 0  0  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2  0 X^2  0  0 X^2  0 X^2  0 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2 X^2  0  0  0 X^2  0  0 X^2  0 X^2 X^2  0 X^2 X^2  0  0  0  0 X^2  0  0 X^2 X^2  0
 0  0  0  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0  0 X^2  0 X^2  0 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2  0 X^2  0  0  0 X^2 X^2  0 X^2  0 X^2 X^2 X^2  0  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2 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+28x^52+40x^53+108x^54+72x^55+87x^56+40x^57+40x^58+24x^59+41x^60+16x^61+12x^62+1x^68+2x^84

The gray image is a linear code over GF(2) with n=224, k=9 and d=104.
This code was found by Heurico 1.16 in 0.077 seconds.