How do I get it? the nameless hero won't grab the ledge of the doorway... see the attached screenshots

Ah, this is a location and chest known to be quite tricky. In the original game, without the add-on, you could simply jump up to the tower, as you tried, and get to it, but in NotR it isn't possible anymore, for whatever reason.
Try this trick: there are a few items that have pretty big 3D models in the game world, on which you can stand. One of them is "Buddlerfleisch". I don't know its name in English, and couldn't find it by a quick search either, sorry. But it is the biggest mushroom you can find, with a gray texture. Alternatively you can try the little gold chest.
It is a bit awkward to get it right, but you can drop the item in the world so that you can stand on it and jump, providing the little extra height you need.

Just for your interest, the chest doesn't contain anything essential, so there isn't much harm in skipping it. Still, I hope this will help you out.

As I always like to say, to the rescue (at least for G2/A). [url=http://mondgesaenge.de/G2ADB/EN/]Digger Meat. ;)