Umm.... the 'daily' rides you see are my bike commutes... 25 miles a day. Plus whatever I do on weekends and after work. Hrmm... I haven't paid for a membership over on that site yet, so it doesn't look like you can see other months, just the current one, so you can't see a lot of my longer rides. The commutes make for a GREAT base mileage, though... I rode all winter long, and started the season in a lot better shape than most of the other riders.
I've put in 4,100 miles so far this year, bringing my 12 month total since I started riding at the end of May of last year to over 10,000 (my goal for the year.
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I ride EVERYWHERE, I have no car.
4 weeks isn't much time to prepare for a 200 mile ride... I started riding with groups and clubs earlier this year, and went from there.
Try to find a club near you that's interested in Randonneuring and see what kind of training rides they have available.
Also, you mention that you're only up to 54 miles, but you don't really say how often you can do those length of rides.... Someone said that if you can comfortably ride the distance every week then you can physically handle the ride, and I think that's pretty true.
In that case, you need to work on the differences between a single really long ride and a bunch of shorter rides... of which there are mainly two:
1) Bike fit. For a shorter ride (or LOTS of short rides), you can deal with a poor fit... on a long ride you'll REALLY regret it if your bike doesn't fit you very well.
2) Nutrition. Keeping yourself fueled and hydrated is EXTREMELY important, and possibly tricky... I just completed my third brevet yesterday (another 300k + extra miles) and I'm just getting the nutrition part down... still working on the hydration.
Tons of advice in this forum and the Training and Nutrition forums... look through it and see what seems applicable.
And good luck on your ride!