Does SQL Server 2014 Express, with Advanced Services, actually support full text search?
There is already an existing answer posted by Aaron Bertrand for SQL Server Express 2012.

First install SQL Server 2014 Express with Advanced Services as you did. Then read Aaron's instructions at:

https://stackoverflow.com/questions/10407337/express-with-advanced-services-cant-create-full-text-index

The short version is that the user interface does not behave properly when setting up full text.  But you can enable and set up Full Text Indexing and Search through T-SQL code.