The phrase "high enough quality" is a correct and usable phrase in written English.
You can use it to describe something that is judged to be of a good or high quality. For example, "The team worked hard to make sure the product met their high enough quality standards."
"This might be because the extra pre-school places were not of high enough quality.
Perhaps if the art produced was of high enough quality, there would not be a problem.
Scientists' reservations pertain to whether the 60 lines of stem cells sanctioned by Mr. Bush are of high enough quality to be useful.
The completed short, "Live Music," has been deemed of high enough quality by Sony Pictures Entertainment to warrant a theatrical run.
In the near future, HD video, or its successor will take high enough quality video that a still from such footage will essentially be a high quality photograph.
This fuels growth in the number of researchers and research projects and the number of articles that are written and are of high enough quality to be published.
Those were just some of the other words she used, while explaining that doctors found her eggs were not of "high enough quality".
Quite a few were submitted for the Booker prize, in fact, and were deemed not of high enough quality to make the long or the short list.
By 1920 the surrounding mines closed because the iron ore being gouged from them was not of a high enough quality.
(Paper can be recycled only about three times before it's no longer high enough quality to use for books; lower quality papers can be recycled about seven times).
Commissioners would have powers to terminate contracts if they judged the private-sector provider was not providing high enough quality care.
