you can get a 212 predator from harbor freight, I hear they're on sale for $99 right now, and if not they go on sale pretty often. You can get one of those and put some performance parts into it. Or if you're looking for something you can just buy and drop in, there is the 420 pred, of you could get a honda GX390 or something of the like.
A problem you're going to run into though is whether or not these larger engines will fit on your mounting plate. Since right now you're running a 150cc , a larger CC will likely have a much larger footprint.
You might be able to find a 125-150CC bike engine to put on there, it'll be the same displacement, but a 2 stroke with a built in trans could get you shifting along pretty quick.