The generator matrix

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

generates a code of length 56 over Z2[X]/(X^3) who´s minimum homogenous weight is 47.

Homogenous weight enumerator: w(x)=1x^0+114x^47+467x^48+706x^49+1091x^50+1644x^51+2113x^52+2498x^53+2775x^54+3240x^55+3287x^56+3282x^57+3117x^58+2578x^59+2155x^60+1478x^61+921x^62+626x^63+341x^64+156x^65+92x^66+50x^67+16x^68+8x^69+4x^70+2x^71+4x^72+2x^79

The gray image is a linear code over GF(2) with n=224, k=15 and d=94.
This code was found by Heurico 1.16 in 33.8 seconds.