Traditionally (as in the early buddhist suttas), enlightenment (understood as nibānna) is reached with the permanent cessation of dukkha. A pre-requisite is the destruction of all fetters. So, nibbāna here has really nothing to do with how still is the mind. Moreover, it is not a temporary experiencestate where the mind is somewhat still.
The word "enlightenment", though, is used in texts of different schools (buddhist and otherwise) to describe different experiences (eg. "satori").