How to add core column "Modified" to a content type

I don't know if this is the correct category to put the question in but if not you're free to move it...

I'm creating a page layout in SharePoint 2013 using SharePoint Designer and the Design Manager, and so far everything seems to be working. But I would like to add the "Modified" site column to my page layout but it is not available in Design Manager as a snippet, likely because the column is not added to the content type. I thought I would be able to simply add the site column in my content type definition as a reference like this:

<FieldRef ID="{28cf69c5-fa48-462a-b5cd-27b6f9d2bd5f}" Name="Modified" />

This has worked for all the custom site columns I have added to the content type but for some reason the "Modified" site column is not added to the content type. Does anyone know why this may be the case? Do I need to add other attributes in the field reference?