The generator matrix

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

generates a code of length 56 over Z2[X]/(X^3) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+10x^54+52x^55+8x^56+40x^57+4x^58+4x^59+6x^60+1x^64+2x^74

The gray image is a linear code over GF(2) with n=224, k=7 and d=108.
This code was found by Heurico 1.11 in 0.062 seconds.