I found a ruling just here
(http://dnd.wizards.com/articles/features/rules-answers-february-2016) in that you have to read the description of the weapon.
In D&D, the first type of magic is part of nature. It is no more dispellable than the wind. A monster like a dragon exists because of that magic-enhanced nature. The second type of magic is what the rules are concerned about. When a rule refers to something being magical, it’s referring to that second type. Determining whether a game feature is magical is straightforward. Ask yourself these questions about the feature:
• Is it a magic item?
• Is it a spell? Or does it let you create the effects of a spell that’s mentioned in its description?
• Is it a spell attack?
• Does its description say it’s magical?
If your answer to any of those questions is yes, the feature is magical.
Further down: (Emphasis mine)
Do magic weapons give you a bonus to attack and damage rolls? A magic weapon gives you a bonus to attack rolls and damage rolls only if its description says it does. Every magic weapon can bypass resistances and immunities to damage from nonmagical attacks, but only certain magic weapons are more accurate and damaging than their nonmagical counterparts. For example, a +1 longsword and a giant slayer both give you a +1 bonus to attack rolls and damage rolls, whereas neither a flame tongue nor a frost brand provides such a bonus. All four weapons, however, can bypass an earth elemental’s resistance to bludgeoning, piercing, and slashing damage from nonmagical attacks.
In short, a bonus to attack rolls and damage rolls is considered a
special property of a magic weapon, not something that all magic
weapons provide automatically.
The jug would satisfy Is it a magic item? thus yes, your jug would class as a magical weapon.
Justifying this is pretty hard for me because for the record I don't agree with this but I have to look at the rules as written! There is nothing the DMHB or PHP that downplays the capabilities of using an improvised weapon from an enchanted point of view, there is nothing to say that an improvised weapon is not a "weapon". After-all a magical longbow hitting someone in melee is classed as improvised from a damage roll point of view - but can anyone argue it isn't a magical weapon? It certainly passes the test from the rule clarification.
The rule clarification I quoted above is not solely concerned with magical weapons either:
Determining whether a game feature is magical is straightforward
Clearly the word "feature" means other than "weapon". Indeed, even the 4 questions to ask fail to mention the word weapon at all - the entire PASSAGE fails to mention "weapon". They all say item. so firstly we determine our weapon; it is an improvised weapon "alchemy jug". Now we determine if it is magical, well it passes the "it is a magic item" therefore we have a magical improvised weapon. so:
Every magic weapon can bypass resistances and immunities to damage from nonmagical attacks
The passage I quoted from the rule clarification was also shown to determine if an attack was magical in nature (dragon breath weapon). the "test" to see if it was clearly states as the first time "is the item magical". It does not state anywhere is it a magical weapon.