The board of supervisors of any drainage district organized under the provisions of sections 31-301 to 31-305 shall cause a topographical survey to be made of the district by some competent engineer. The engineer shall make a complete topographical survey of the district and submit the same to the board of supervisors with maps and profiles of such survey and a full and complete plan for draining, reclaiming, and protecting the lands in the district from the overflow of, or damage by water or floods. The survey shall show the physical characteristics and location of any right-of-way, roadbed, bridge or bridges and other property or improvements in the district belonging to or under the control of any railroad company. The engineer shall report the location of any and all public highways which may be crossed by the right-of-way of any ditch, levee, or other improvement planned for the district.