It's totally up to you however I would consider a few things.
- The need to hire and train your replacement is not your problem. It is the company's problem and a normal part of business
- Does providing a longer notice hurt you in any way with the new company? Or are you postponing new and better pay? Benefits? If so, stick to the standard 2 weeks.
In general, a notice is a professional courtesy and nothing more except in your case where you are contractually required to provide 2 weeks. There is little to gain other than being a "nice guy" by providing more.