The generator matrix

 1  0  1  1  1 X^3+X^2+X  1  X  1 X^3+X^2  1  1  1  1 X^3  1 X^3+X^2+X  1  1  1 X^2+X  1 X^2  1 X^3+X  1  1  1  1  1 X^2  1  1  1 X^2+X  1  1  1  1  1  1 X^3+X^2+X  X  1  1  X  1  1  X  X  1  1  1 X^3+X  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^2+X X^2+1  X X^3+1  1  0  1 X^3+X+1 X^3+X  1  1 X^3  1 X^2+1  1 X^2 X^3+1 X+1 X^3+X^2+X+1 X^3+X  1  1 X^2+X+1 X^2  1 X^3+1 X+1 X^2+X+1 X^2+X+1 X^3+X^2+1 X^2  1  X X^3+X^2+X+1 X^2+X+1 X^3  1 X^2+X+1 X^3+X^2  1 X^2+X X^3+X^2+1 X^3+X^2  1  0
 0  0 X^2  0 X^3+X^2 X^2  0 X^2 X^3+X^2 X^3 X^2  0 X^3+X^2 X^3 X^3+X^2 X^3 X^3+X^2 X^3+X^2 X^3 X^2  0 X^2 X^2  0 X^3 X^3+X^2 X^3  0  0  0 X^3+X^2 X^2 X^2 X^3+X^2 X^3 X^2 X^3 X^2 X^3 X^3+X^2 X^3+X^2 X^3 X^3  0  0 X^3+X^2 X^3+X^2 X^2 X^2 X^2 X^3  0  0 X^3  0
 0  0  0 X^3  0  0  0  0 X^3  0  0 X^3  0 X^3 X^3 X^3 X^3 X^3  0 X^3 X^3 X^3  0  0 X^3 X^3  0  0 X^3  0  0  0  0  0  0 X^3 X^3 X^3 X^3 X^3  0  0 X^3 X^3  0 X^3 X^3  0 X^3  0  0 X^3 X^3  0  0
 0  0  0  0 X^3  0 X^3 X^3  0 X^3 X^3 X^3  0  0 X^3 X^3  0 X^3 X^3 X^3  0  0  0 X^3 X^3 X^3  0  0 X^3  0 X^3  0 X^3 X^3 X^3  0  0 X^3 X^3  0  0  0  0  0 X^3 X^3 X^3  0  0  0  0  0 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+67x^50+272x^51+329x^52+614x^53+407x^54+848x^55+383x^56+562x^57+233x^58+224x^59+86x^60+28x^61+23x^62+10x^65+2x^66+2x^69+2x^70+2x^74+1x^76

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 0.296 seconds.