How about telling people that they should treat the office area as if they were at the library? Well kept libraries are fairly silent places because everybody knows that they should keep their voices down and not unnecessarily disturb the visitors.

You could lead by example by keeping a low voice and going to a meeting room if you need to have a long discussion with someone.

Your superiors probably wouldn't be fond of the idea. Whispering isn't natural to them and having them adapt to the programmers, which they out rank, would be tough.