you need to know what code and what protocol your remote is working with. Looking at your examples it could be Manchester coding. But there are further methods used by other remotes, i.e. pulse width.
Some time ago I researched about wheater sensors the result of which is attached as word document - in German.
For Oregon Scientific sensors an Arduino sketch also is attached.
If your remote is not contained in the word document then internet search should help.
WeatherSensors.zip (770.0 KB)