Transitive verb: To enroll someone in a class.
Intransitive verb: To enroll (oneself) in a class.
Passive: To be enrolled in a class at a college / university.
I wouldn't really say "enroll in a university/college" because usually you apply to a university and are either accepted / rejected. Enrolling, to me, has this feeling that you control the process. You don't really control this for a university/college, so it sounds a bit odd, but is still completely understandable. This may be a difference between British / US English.
I would say (1 = most formal, 4 = least formal)
1) "She applied to and was accepted at ABC University, where she earned a doctorate after four years of study."
2) "She went to ABC University and graduated with a doctorate after four years."
3) "She went to college at ABC University and got her doctorate there after four years."
4) "She went to college and got her doctorate after four years."
Also, in US English, we use "college" instead of "university". "I am going to college", "In college, I studied ____". We do use "university" if it is part of a larger name, e.g. "The University of Texas at Austin" or if we're specifically distinguishing between the technical definition between a college and a university (a university is made of up colleges).
Because we say "The University of ________" most of the time, it sounds very British to say, "At university, I studied _______" -- the American ear expects "a" or "the" before "university". It's perfectly understandable, it just sounds a bit odd, and no doubt they perceive "at college" likewise to be odd.