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  0  1  1 X^2+X  1  1  1  1 X^2  X  1  1  1  1  1  1  1  1  1  1  1  1 X^2  X X^2  X X^2  X  1  1  1  1  1  1  X  X
 0  1 X+1 X^2+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+1  1 X^2+X X^2+1  1 X^2  X X^2+X+1  1  1  1 X^2  X X^2  X X^2  X X^2+X+1  1 X^2+X+1  1 X^2+X+1  1  1  1  1  1  1  1  0 X^2+X  0 X^2+X  0 X^2 X^2+X X^2+X
 0  0 X^2  0 X^2  0 X^2  0 X^2 X^2  0 X^2  0  0  0 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0  0  0  0 X^2 X^2  0  0  0  0 X^2 X^2  0  0  0  0 X^2 X^2  0 X^2  0  0
 0  0  0 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2  0  0  0  0 X^2  0 X^2  0 X^2 X^2  0 X^2  0  0 X^2 X^2  0 X^2  0  0 X^2 X^2  0 X^2  0  0 X^2  0 X^2 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+56x^54+138x^56+56x^58+2x^60+1x^64+2x^76

The gray image is a linear code over GF(2) with n=224, k=8 and d=108.
This code was found by Heurico 1.16 in 0.0672 seconds.