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

generates a code of length 56 over Z2[X]/(X^3) who´s minimum homogenous weight is 46.

Homogenous weight enumerator: w(x)=1x^0+47x^46+82x^47+171x^48+212x^49+274x^50+348x^51+475x^52+566x^53+671x^54+852x^55+836x^56+872x^57+722x^58+580x^59+422x^60+300x^61+245x^62+150x^63+122x^64+84x^65+83x^66+32x^67+15x^68+14x^69+5x^70+4x^71+6x^72+1x^82

The gray image is a linear code over GF(2) with n=224, k=13 and d=92.
This code was found by Heurico 1.16 in 4.6 seconds.