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

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+260x^46+563x^48+48x^49+904x^50+200x^51+1301x^52+652x^53+2032x^54+1144x^55+2252x^56+1148x^57+1980x^58+664x^59+1356x^60+196x^61+832x^62+40x^63+454x^64+4x^65+236x^66+86x^68+28x^70+2x^72+1x^84

The gray image is a linear code over GF(2) with n=224, k=14 and d=92.
This code was found by Heurico 1.16 in 43.9 seconds.