I can see weathered wood more than a weathered plaster surface, but that is individual. You could, for example, drill battens onto the current wall and then screw narrow boards to them (I once did something like this with roof battens). It looks like rhombus slats and you can do it lengthwise or crosswise, for example paint it gray or leave it raw and let it weather like often seen with wooden facades on houses. For cost reasons and also because in my opinion it can look good, I would use rough-sawn timber. Because of the length of 12m, I might divide it with 3 or 4 square, tall plant troughs, which you can also make out of wood or there are nice ones in natural stone or concrete look. I had the same experience with the steam cleaner, although for me the soil always got back onto the wall and it looked dirty again immediately, as did from the rain. Then you would have to have a small strip of gravel or something like that to avoid this. As I said, this is an idea that you would first have to like. I wanted to do it myself – it is very easy, I like working with wood and also like to look at it, plus it is always easy to repair and I didn’t want to spend a fortune on it. A continuous wall made of such stones would be too massive for me; as I said, I would somehow also break that up with the wood.