Depends on the point of the person asking and the person answering.
If you say this Wednesday, I would assume this coming Wednesday; especially if today is Sunday and you are conveying some info as to an event that will happen.
I have been a teacher in Japan for the past 15 years ,and for the Japanese , it's pretty hard for them to discern future events as well as coming events in English. So for them everything is last or now. This past weekend is a pain for them, the weekend after next goes right over their head.
Please, if you are going to convey this Wednesday, convey it so there is no confusion. This past Wednesday, or next Wednesday.