The Malcorian warp ship was the prototype of the Malcorian Space Bureau's first Malcorian warp driven starship that was scheduled for launch in the late 2360s. Its first planned destination according to Malcor III's Space Administrator Mirasta Yale was to be the nearby Garth system.
However, an unfortunate first contact between the Malcorian government and the crew of the USS Enterprise-D in 2367 led to increased levels of xenophobia on behalf of the conservative minded Chancellor Avel Durken. The Malcorian space program was consequently delayed while the government focused on more domestic issues. (TNG: "First Contact")
Background information Edit
The display model of the Malcorian warp ship, seen in Space Administrator Mirasta Yale's office, was one of the few starship designs in the Star Trek franchise that was conceived as such, not having been featured as an in-universe fully realized "real" starship. Scenic Art Supervisor Mike Okuda recalled on the design, "My recollection is that I designed the Malcorian ship desktop model, but it is possible that it may have been Rick, who designed most of the ships and props...I think Ed Miarecki built it for us. Don't know what happened to it...I know I did the animated computer readouts in the lab. A big silkscreened diagram of the ship also appears on a clear acrylic display in the lab. Yes, it was specifically done for this episode, although the model did later appear as set dressing in another episode."
Confirming that he was indeed at least the co-designer, Senior Illustrator Rick Sternbach added, "I think I did a few doodles or 3D computer model roughs of this one, based amazingly vaguely on a mashup of a Bussard ramjet and an Enzmann giant deuterium fuel tank starship. I do believe Mike added the warp nacelles and offset them from the center framework, which may have hinted at the possibility that warp physics was similarly discovered and refined by separate cultures." 
The other episode, Mike Okuda referred to was Star Trek: The Next Generation' sixth season episode, "Tapestry", were the model was in a similar function reused as set dressing in the quarters of recently graduated Ensign Jean-Luc Picard in the by Q recreated reality.