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

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+185x^48+4x^49+218x^50+44x^51+398x^52+164x^53+490x^54+300x^55+572x^56+300x^57+476x^58+164x^59+340x^60+44x^61+172x^62+4x^63+136x^64+42x^66+27x^68+10x^70+2x^72+2x^76+1x^84

The gray image is a linear code over GF(2) with n=224, k=12 and d=96.
This code was found by Heurico 1.16 in 18.4 seconds.