It is possible to set up your property search parameters so you are only looking at TH's that fit this description. It will save you a ton of time.
Finding a fenced in backyard for a TH will be pretty much impossible though depending on the area you are looking for. Going the Twin Home route may be the ticket for you instead.
If you want I pasted a property search website below where you 100% can control your private search parameters. If you have any questions just contact me sometime and I will be able to tell you where to search.
I have the perfect townhouse for you. It is surrounded on two sides by open area that will never be built on and has a private patio out the back. Give me a call and we'll set up a time to get you over there.