The generator matrix

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

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+49x^50+248x^51+398x^52+550x^53+596x^54+514x^55+620x^56+492x^57+290x^58+200x^59+58x^60+30x^61+19x^62+10x^63+11x^64+5x^66+4x^67+1x^78

The gray image is a linear code over GF(2) with n=440, k=12 and d=200.
This code was found by Heurico 1.16 in 0.265 seconds.