The generator matrix

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

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+83x^52+244x^53+283x^54+376x^55+113x^56+352x^57+255x^58+238x^59+91x^60+4x^61+2x^62+2x^66+2x^67+1x^70+1x^90

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 0.188 seconds.