BBI-993 type starship
The BBI-993 was a type of Earth starship that was utilized during the 22nd century. They were in use as early as 2137. (TNG: "Up The Long Ladder", okudagram)
The name of this ship type was mentioned in a list of ships that were launched from Earth, with destinations in or near to the Ficus sector, between the years 2123 and 2190. This list was displayed on Jean-Luc Picard's desk monitor in his ready room aboard the USS Enterprise-D. A legible version of the okudagram first appeared in the reference book, Star Trek: The Next Generation - The Continuing Mission. The list became legible to viewers with the remastered episode.
BBI-993 was an in-joke reference to the movie The Adventures of Buckaroo Banzai Across the 8th Dimension.
Given that the class predates the breaking of the Warp 2 barrier in 2143, it was presumably slower then warp 2.