Unfortunately there is no way of doing this with JavaScript / SharePoint Client Site Object model. The support is just not there.
Is there a reason why it must be at the farm level? Could it be placed at the web application level at all?
Short of that, a custom solution will need to be developed, either with a web service, httphandler or another custom way of accessing the data at the farm level.
There is a small sample in the thread at
http://sharepoint.stackexchange.com/questions/36945/how-to-access-a-web-application-farm-level-property-bag-via-jquery-javascript-cl[
^] which shows how to create a method in a web service which is then called by javascript via the SPServices (
http://spservices.codeplex.com[
^])
A great read is : Choose the right API set in SharePoint 2013 -
https://msdn.microsoft.com/en-us/library/office/jj164060.aspx[
^]
Hope this helps