The generator matrix

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

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+52x^49+136x^50+244x^51+334x^52+376x^53+388x^54+380x^55+380x^56+398x^57+411x^58+320x^59+251x^60+178x^61+72x^62+60x^63+46x^64+14x^65+9x^66+20x^67+11x^68+6x^69+7x^70+1x^72+1x^78

The gray image is a linear code over GF(2) with n=224, k=12 and d=98.
This code was found by Heurico 1.16 in 0.774 seconds.