Information is just how we perceive and try to understand things, and data is just sets of physical matters put together to portray information in ways that we understand. Therefore it's more psychological than physical since our perception of things is governed by how our brain and mind works.
Physical matters can be used to store and portray data or information, but data or information themselves can't materialize into physical objects unless there is an instrument, with sets of parameters, that works on constructing physical objects based off those data or information.
Say, a brick tower is 3 meters tall and weighs 10 kilograms. That information can't materialize into physical objects by itself. But we can use physical objects to store that information, and from that information we can materialize that information into physical objects by building the said tower, or by creating a machine that can build it.
You do need physical matters to store data and information, though, (A piece of paper, electronic storage, our brain) and to convey it (light, soundwave, radio wave, electronic means, and the likes)
Everything is physical, even those that are oftenly called as metaphysical need physical matters to exist.