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  X  1 X^2  1  1  1  1  1  1  1  1  X  1  X  1  0  1 X^3+X^2  1  1  0  1  X  X  0
 0  X  0  X X^3  0 X^3+X  X X^2 X^2+X X^2 X^2+X X^3+X^2 X^2 X^3+X^2+X X^2+X  0 X^3 X^3+X X^3+X  0 X^2 X^3+X X^2+X X^2 X^3+X^2+X X^3 X^3+X^2 X^2 X^2+X  X X^3+X X^2+X  X  0 X^3+X X^3+X^2+X X^3+X^2+X  0 X^2+X X^3+X^2 X^2 X^3+X X^3+X X^2+X X^3+X^2+X X^3 X^2 X^3  X X^2+X X^3+X^2  0 X^3  X  X
 0  0  X  X X^2 X^2+X X^2+X X^2 X^2 X^3+X^2+X  X X^3+X^2  0 X^2+X X^3+X X^3  0 X^3+X^2+X X^2+X X^3+X^2 X^3+X^2 X^2+X X^3+X X^3+X^2 X^3+X^2 X^3+X^2+X X^3+X  0 X^3+X  0 X^3 X^3+X^2+X X^3+X X^3+X X^2  0 X^3  X X^3+X^2+X X^2+X X^2 X^3 X^3  0 X^2+X X^3+X^2  X X^3+X^2  X X^3+X^2 X^2  X X^3+X^2+X  X  X  0
 0  0  0 X^3 X^3 X^3  0 X^3  0 X^3 X^3  0 X^3  0  0 X^3 X^3  0 X^3  0  0 X^3  0 X^3 X^3  0 X^3  0  0  0 X^3 X^3 X^3  0  0 X^3  0 X^3  0  0 X^3  0 X^3  0 X^3  0  0  0 X^3 X^3 X^3 X^3 X^3  0  0 X^3

generates a code of length 56 over Z2[X]/(X^4) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+160x^52+112x^53+308x^54+312x^55+415x^56+224x^57+244x^58+96x^59+82x^60+16x^61+52x^62+8x^63+12x^64+4x^66+1x^68+1x^92

The gray image is a linear code over GF(2) with n=448, k=11 and d=208.
This code was found by Heurico 1.16 in 0.204 seconds.