These are the episodes of Star Trek for which Gene Roddenberry received a sole teleplay credit:
The Menagerie, Part I
The Menagerie, Part II
A Private Little War
The Omega Glory
These are the episodes for which he shared a credit with another writer:
Bread and Circuses (with Gene L. Coon)
The Savage Curtain (with Arthur Heineman)
Encounter at Farpoint (with D.C. Fontana)
Hide and Q (with Maurice Hurley)
Datalore (with Robert Lewin)
The episodes listed uptopic which are not included here are those for which the teleplay is credited to other writers and Roddenberry received a sole or shared "story by" credit.
As I mentioned before, a "story" can be anything from a one or two sentence premise to several pages. With rare exceptions scene breakdowns, detailed action, dialogue and character development are inherent in the teleplay itself. The teleplay is the actual script, the blueprint from which the episode is budgeted and produced. WGA contracts establish much higher payments and percentages of residuals for the author(s) of teleplays than for those awarded story credit alone.
BTW, I searched using the list of episodes presented uptopic as my basis. Therefore, if there are episodes that Roddenberry was credited for that were not in that list I've missed them in mine as well.