My school computers have OS X 10.9.4 on them but they don't want to update them because of incompatibility with their Music class software. From what I see on Apple's website Xcode 6.4 and 6.3.1 both need Yosemite. Is there another version of Xcode that I can download somewhere so I can code using Swift?
A quick search for Xcode at the Wikipedia give you the answer. With the OS X version 10.9.4, you are able to install Xcode 6.2 and below.
On Xcode 6.2 you can code in Swift, but I'm afraid is not the latest Swift version.