The generator matrix

 1  0  1  1  1 X^3+X^2+X  1  X  1 X^3  1  1 X^2  1  1  1 X^2+X  1  1 X^3+X^2  1 X^3+X  1  1  1  1  1  1  1  1 X^3+X^2  1  1 X^3+X  1  1 X^2+X  1  1  0  1  1  1  X  X X^3 X^2  1  1  1  1  1  1  1  1  1
 0  1 X+1 X^2+X X^3+X^2+1  1 X^3+X^2  1 X^2+X+1  1 X^3+X  1  1 X^3 X+1 X^3+X^2+X  1 X^3+X^2+X+1 X^2  1  X  1 X+1 X^3+X^2+X+1 X^2+1 X^3+1 X^2+1 X^3+1 X^3+X+1 X^3  1 X^3+X^2+X+1 X^3+X^2+X  1 X^3+X^2+1 X^2  1 X^2+1  X  1 X+1  1 X^3+1 X^2+X X^3+X  1  1 X^3+X+1 X^2+X X^3+X X^2+X+1 X^3+X+1 X^3+X^2+1 X^3+X^2+1 X+1 X+1
 0  0 X^2  0 X^3+X^2 X^2  0 X^2 X^3+X^2 X^3+X^2  0 X^2 X^3+X^2 X^2 X^3 X^3+X^2  0 X^3 X^2  0 X^3+X^2  0 X^3 X^3  0 X^3 X^3  0 X^2 X^2  0 X^3+X^2 X^3+X^2  0 X^2 X^3+X^2 X^3 X^3+X^2 X^2 X^3 X^3 X^3  0 X^3 X^3+X^2 X^3+X^2 X^2 X^3+X^2  0 X^3 X^3  0 X^3+X^2 X^3+X^2 X^2 X^3+X^2
 0  0  0 X^3  0  0  0  0 X^3 X^3 X^3 X^3 X^3  0 X^3 X^3 X^3  0 X^3 X^3  0  0 X^3  0  0 X^3 X^3  0  0  0 X^3 X^3 X^3  0  0 X^3 X^3 X^3  0  0  0  0 X^3 X^3  0  0  0 X^3  0  0 X^3 X^3 X^3  0 X^3 X^3
 0  0  0  0 X^3  0 X^3 X^3  0  0 X^3 X^3 X^3 X^3  0 X^3  0  0  0 X^3  0 X^3 X^3 X^3  0 X^3  0 X^3 X^3  0  0 X^3  0  0  0 X^3 X^3  0 X^3 X^3 X^3  0 X^3  0 X^3 X^3  0  0  0 X^3  0  0 X^3  0 X^3 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+389x^52+240x^53+538x^54+576x^55+763x^56+480x^57+550x^58+192x^59+237x^60+48x^61+54x^62+14x^64+2x^66+2x^68+8x^70+2x^80

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 49.6 seconds.