The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X X^2 1 1 1 X 1 1 1 1 X^2 1 1 X 1 1 1 X^2 1 X 1 X 1 0 X 0 0 1 X^2 1 1
0 X 0 0 0 0 0 X^2 X^2 X X^2+X X X X X^2+X X 0 X^2+X X^2 X X^2 X 0 X X^2 X^2+X X^2 X^2+X X^2+X X^2 X X^2 X 0 X^2+X X 0 X^2 0 X^2+X X^2+X 0 0 X^2 X^2 X X^2 X 0 X^2 X X^2 X^2 X^2 0 X^2+X
0 0 X 0 0 X^2 X^2+X X X X X X X^2+X 0 0 0 X^2 X^2 X^2+X X X^2 0 0 X^2+X X^2 0 0 X^2 0 X^2+X 0 X X X^2+X X^2+X X^2+X X^2 X X X X^2+X X^2 X X^2 X^2 X^2 X^2 X^2+X 0 X X^2+X X X^2 X X^2 X
0 0 0 X 0 X^2+X X^2+X X X^2 X^2+X X^2+X 0 0 X X X^2 X X^2 X^2+X 0 X^2+X 0 X^2 X X^2 0 X X X X X X^2 X X^2 0 X^2 0 X X^2+X X^2 0 X 0 X^2+X X^2 0 X X^2+X X X 0 X^2+X 0 X X 0
0 0 0 0 X X X^2 X^2+X X X^2+X X^2 X^2 X X^2 X^2+X X X X^2 X^2 X^2+X 0 X^2+X 0 X^2+X X^2+X X^2 X X^2+X 0 X X^2 X^2 X^2 X 0 0 X^2 X^2 X X^2 X^2+X X^2 X X^2 X X^2+X X X X^2 X X^2 X 0 0 0 X
generates a code of length 56 over Z2[X]/(X^3) who´s minimum homogenous weight is 49.
Homogenous weight enumerator: w(x)=1x^0+32x^49+78x^50+136x^51+137x^52+188x^53+215x^54+210x^55+228x^56+156x^57+169x^58+148x^59+108x^60+76x^61+34x^62+36x^63+31x^64+20x^65+12x^66+12x^67+7x^68+8x^69+2x^70+2x^71+1x^74+1x^86
The gray image is a linear code over GF(2) with n=224, k=11 and d=98.
This code was found by Heurico 1.16 in 0.307 seconds.