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

generates a code of length 56 over Z2[X]/(X^4) who´s minimum homogenous weight is 50.

Homogenous weight enumerator: w(x)=1x^0+57x^50+81x^52+64x^53+99x^54+128x^55+1256x^56+64x^57+185x^58+29x^60+33x^62+34x^64+10x^66+6x^68+1x^104

The gray image is a linear code over GF(2) with n=448, k=11 and d=200.
This code was found by Heurico 1.16 in 0.344 seconds.