The generator matrix

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

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+56x^53+156x^54+68x^55+52x^56+24x^57+68x^58+16x^59+22x^60+16x^61+16x^62+12x^63+3x^64+2x^68

The gray image is a linear code over GF(2) with n=224, k=9 and d=106.
This code was found by Heurico 1.11 in 0.047 seconds.