After calling my home depot, a 2100 by 1000 by 36 mm conifer wood door made from wooden boards with a double Z reinforcement on the back is available with a weight of 25 kilos. That's roundabout 55 lbs for a 7' by 3 1/3' by 1.5" item. I guess that's kinda heavy. But that mass and bulk is anyway only relevant for carrying capacity. However, ask your GM for what your specific door comes down to in weight and measurements.
However, how to model it?! Actually, that's rather easy: We should look at what kind of weapon it resembles most: A mantlet, pavise, or if cut to size, a tower shield1.
Now, how does 5th edition handle these?
A deployed mantlet or its smaller cousin, the pavise, is nothing else but a wooden wall, offering the advantage of anything between full cover to half cover, depending on its size and if one ducks behind it. In other words: treat it as a wall of some height. If the GM agrees, it can be moved by spending movement to push or carry an item of somewhat equivalent weight. However, that use is not really compatible with a weapon used for bashing people, in fact, you technically can't wield a wall as a weapon and thus not attack with it at all.
So let's look at the next contender: tower shields.
While the only item described as a tower shield in 5e is the fluff for a magic artifact (battering shield), tower shields are (unless homebrewed by the GM) handled like any other type of shield. This enables us on a homebrew-free basis to assume all the normal stats and rules for any shield and just describe it as a tower shield... eh, door-shield.
As a direct result, clobbering people with the door-shield is best done by either using the Shield Bash maneuver or handling it as an improvised weapon.
1 - Looking up at my LARP suppliers, they offer a roman Scutum weighing about 5 kilos or 11 lbs. But for anything but hauling, that's irrelevant in combat under 5E rules. However, the GM might feel inclined to modify the shield's values to account for the larger size of a door compared to a Scutum and its higher weight. But that's a GM ruling then.