It's hard to imagine what you think you will hear at that frequency, but there is nothing illegal about building a receiver that I know of.
At such frequencies the propagation is usually so poor that you have to wait for a really dry day, and use parabolic dish antennas aimed with a rifle scopes to get a useable signal at more than a mile or so.
If you were successful in constructing such a receiver it is doubtful you would hear anything coming through and you would quickly become bored with the whole affair.
My cost estimate for this receiver would be about $7000 - $ 10,000 including the research, fabrication of the components, and purchase of the required parts. It would look like an antenna, a down converter, and a purchased general coverage receiver like an R-2000 which goes up to about 2 GHz.