The generator matrix

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

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+20x^54+68x^55+88x^56+56x^57+10x^58+4x^59+6x^60+1x^64+2x^78

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 0.0668 seconds.