Warforged are Constructs, right?

As I was looking at the Warforged, a though came into my mind.
Warforged are Constructs with the Living Construct subtype.
In the stats for Warforged, they list everything that a construct gets that a living construct does not get.
What I did not see is any mention of a construct's bonus hit points.

As per the SRD:
-Because its body is a mass of unliving matter, a construct is hard to destroy. It gains bonus hit points based on size, as shown on the following table.
Construct Size Bonus Hit Points
Medium 20

Construct get these bonus hit points to make up for having no Con scores.
This would seem that a warforges should have 20 bonus hit points. Obviously this would be pretty overpowering for a player character to have on a +0 LA race. Does it state anywhere that a living construct does not get the bonus hit points?

Construct get these bonus hit points to make up for having no Con scores.

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Unlike other constructs, a warforged has a Constitution score, plus they have a +2 racial modifier to Constitution. And no, they do not gain bonus hp's as the construct does.

Because its body is a mass of unliving matter

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As you just quoted the SRD states unliving matter, yet the warforged is considered a living construct, therefore nixing the whole bonus hp's idea.