

The module's documentation should have details about PCB requirements - in particular, "keep-out" areas and ground planes ...
You need to remove the GND plane under the antenna:
You must also remove the copper from the two mounting holes and only use plastic mounting screws.
Any metal, water, or other 2.4GHz opaque materials will affect the antenna negatively.
The module's datasheet does not specify layout at all, this one's on the module vendor. http://aconno.de/wp-content/uploads/2016/10/ACN52832-Data-Sheet.pdf
Thank you for your answer. Do you know a good source from where I could follow up on this? An article or such.
Not any one in particular, but a searchable keyword is '2.4GHz antenna design' and '2.4GHz printed antenna design'. The type of antenna that your module uses is a printed quarter wave meandering antenna.
Another slightly related topic is 'microstrip' and 'stripline'.