Are unit-tests needed when you have code contracts?

If you're developing application using the code contracts, you may know, that this concept was introduced in Eiffel programming language.

I have become very confused after trying this concept in my C# application using System.Diagnostics.Contracts.

The main question for me is the next:

Are unit-tests really needed, if you have code contracts?

One of the major differences, that unit-test frameworks usually don't provide, is the possibility to call private methods (except MS fakes library with its shims). It's done, because of supporting composition & the idea, that private methods are covered by public method calls.

As for the code contracts, I can declare Contract.Requires, Contract.Ensures for private methods.

So, why do I need unit-testing, when I have code-contracts, which behavior is very similar.

Thanks