MP4 files already use a highly compressive codec like H.264, thus further compressing the video will get you more loss of visual quality.
Do you know, what resolution and length and frame rate the video has? If so post that info. If not, go to QuickTime Player and open the file there and press CMD+I to get the Movie Inspector.
In there you find
The bit rate suggests a 110 minutes long video, which is okay for that size, albeit not being HD, as the name of the file suggests.
If you really need to shrink the video, you can use HandBrake and set the Average Bitrate to around 512 or 768 Kbps and get a file of about 600 MB in size.
If you want an even smaller file and do not mind losing visual quality, experiment.