The statute prohibits sending text messages while operating a motor vehicle on a road. Operating is not defined. In some contexts it means to be in actual physical control of a motor vehicle whether or not it is moving. In other contexts it only means being in control of the vehicle only when it is moving. The best practice is not to text if you are in your vehicle.
Here is the relevant law for your reference:
http://le.utah.gov/code/TITLE41/htm/41_06a171600.htm
This law has been revised a few times, so if you have a legal issue from an alleged past violation, your arguments may be different.