The generator matrix

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

generates a code of length 55 over Z2[X]/(X^4) who´s minimum homogenous weight is 50.

Homogenous weight enumerator: w(x)=1x^0+63x^50+60x^51+208x^52+198x^53+323x^54+412x^55+338x^56+170x^57+133x^58+36x^59+36x^60+10x^61+40x^62+4x^63+9x^64+6x^65+1x^94

The gray image is a linear code over GF(2) with n=440, k=11 and d=200.
This code was found by Heurico 1.16 in 0.25 seconds.