Homesick is a beautiful exploration game. Unfortunately there is no official support for higher then 1440p resolutions such as 4k. Luckily you can edit the config files to set any resolution you want:

1. Go to the Application directory. Default: C:\Program Files (x86)\Steam\steamapps\common\Homesick\UDKGame\Config
2. Edit UDKSystemSettings.ini
3. Change the resolution as you please, for example:
   ResX=3840
   ResY=2160
   
4. Save, launch the game and don’t change any settings in-game.

Enjoy! While you are at it you can also use this and the adjacent config files to make further adjustments to the game. Remember to make a backup beforehand though.