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

generates a code of length 56 over Z2[X]/(X^3) who´s minimum homogenous weight is 48.

Homogenous weight enumerator: w(x)=1x^0+51x^48+46x^49+65x^50+78x^51+175x^52+70x^53+320x^54+80x^55+346x^56+62x^57+296x^58+56x^59+166x^60+58x^61+58x^62+40x^63+26x^64+20x^65+21x^66+2x^67+3x^68+6x^70+1x^74+1x^90

The gray image is a linear code over GF(2) with n=224, k=11 and d=96.
This code was found by Heurico 1.16 in 0.346 seconds.