The generator matrix

 1  0  0  1  1  1 X^3  1  1  1  1 X^2  0 X^3+X^2+X  1  1 X^3+X  1  X  1 X^3+X^2+X  1  0  1 X^3+X X^3+X^2  1 X^3+X^2+X  1  1  1 X^2+X  1 X^2  1 X^3  1  1 X^3+X^2  X  X X^3+X^2+X  1 X^3+X  1  1 X^3+X^2  0  1 X^3+X^2+X X^2  X  1  1  1  1
 0  1  0 X^3 X^2+1 X^3+X^2+1  1  X X^3+X X^3+X^2+X+1 X^2+X+1  1  1 X^2+X  1 X^3+X  1 X^2  0 X^2+X+1  1 X^3+X^2+X+1 X^2  X  1  1 X^3  1  0 X^2+1 X^2  1 X^3+X+1  X X+1  1 X^3+1 X^3+X^2+X X^2 X^3+X  1  1  1 X^2 X^3+X^2+X+1 X^3+X^2+X X^2+X X^3+X^2+X  X X^3  1 X^3+X^2+X X+1  1 X+1  0
 0  0  1 X^3+X+1 X+1 X^3 X^3+X+1 X^3+X X^3+1  1  X  1 X^3+X  1 X^3+X^2+1 X^2+X+1 X^2 X^3+X^2+X  1 X^2 X^3+X+1 X+1  1 X^3 X^3+X^2+X X+1 X^3+X^2+1 X^3+X^2+X X^3+X^2+X  X X^3+X^2  1 X^2  1 X^2+X+1  1 X^3+X^2+X+1 X^2  1  1 X^2+X+1 X^2+1  1  1 X^2+1 X^3+X+1  1  1 X^2+X  1 X^3+X^2+X  1 X^3+1 X^2+X X^3+X^2+X+1  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+100x^52+516x^53+738x^54+616x^55+649x^56+516x^57+279x^58+228x^59+194x^60+120x^61+60x^62+52x^63+24x^64+2x^70+1x^74

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 1.66 seconds.