How can I get my 13 inch MBP (A1425) to display 4k? I just got this monitor, http://www.amazon.com/Seiki-SE39UY04-39-Inch-Ultra-120Hz/dp/B00DOPGO2G

When I  plug it into my MBP's HDMI port, the highest resolution I can choose on it under the "scaled" option is 1080p. Why is this? I've upgraded OSX to 10.9.3 but it has not helped me at all. Any ideas? I've also tried using a thunderbolt to hdmi adapter but that didn't work either.
Straight from the Apple Spec Sheet for that model:


  Dual display and video mirroring: Simultaneously supports full native resolution on the built-in display and up to 2560 by 1600 pixels on up to two external displays, at millions of colors


Looks like that model does not support 4K displays