The generator matrix

 1  0  1  1 X^2  1  1  1 X^2+X  1  1  0 X^3+X  1  1  1  1 X^2 X^3+X^2+X  1  1  X  1  1  X  1  1 X^2 X^3  X  1  1  1  1  1  1  1  1  0 X^3+X^2+X X^3  1  1  1 X^2  1  X  1  1  1 X^3+X X^2+X  1  1  1  1
 0  1  1 X^2+X  1 X^2+X+1 X^2 X^3+1  1 X+1 X^3+X^2+X  1  1  0 X^3+X^2+1 X^3 X^3+1  1  1 X^3+X^2+1 X^2+X+1  1 X^3+X^2  X  1  X X+1  1  1  1 X^3+X^2+X+1 X^2+1  0 X^3+X^2 X^3+X^2 X^3+X+1 X^3+X X^3+X^2+X  1  1  1 X^2+X X^2+X+1 X^3+1  1  0  1 X^2+X+1  1 X^3+X^2+X+1  1  1 X^2 X^3+X^2+X+1  1 X^2+X
 0  0  X  0 X^3+X  X X^3+X X^3  0 X^3 X^3+X X^3+X^2+X X^2 X^3+X^2 X^3+X^2 X^3+X^2+X X^3+X^2+X X^2+X X^3+X^2  X X^3+X^2  X  0 X^3+X^2+X  0 X^3+X^2 X^3+X^2+X  X X^3+X^2 X^3+X^2+X X^3  0 X^3+X X^2+X X^2 X^2+X X^3+X^2+X X^3+X^2 X^3+X^2+X  X X^3 X^3 X^3+X^2 X^2 X^3+X^2 X^3+X^2+X  X X^3+X X^3+X^2+X X^3+X^2+X  0 X^2+X  0 X^3 X^2  0
 0  0  0 X^3  0 X^3 X^3 X^3 X^3  0  0 X^3 X^3  0 X^3 X^3  0  0  0 X^3  0 X^3 X^3  0  0 X^3 X^3 X^3 X^3  0 X^3  0 X^3 X^3 X^3  0 X^3  0  0 X^3 X^3  0 X^3  0  0  0  0  0 X^3 X^3 X^3 X^3  0  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+232x^52+454x^53+629x^54+540x^55+537x^56+512x^57+528x^58+372x^59+205x^60+18x^61+21x^62+16x^63+12x^64+8x^65+4x^66+4x^68+2x^74+1x^76

The gray image is a linear code over GF(2) with n=448, k=12 and d=208.
This code was found by Heurico 1.16 in 0.297 seconds.