Whenever a highway crossing any draining ditch of a drainage district governed by ch. 88 is being constructed or reconstructed or a culvert in any such ditch is being replaced, the highway authority in charge of such work shall consult with the drainage board having jurisdiction of such district for the purpose of determining the depth at which such drainage ditch was laid out. If any culvert or similar opening in a highway is installed at a grade higher than the depth at which such drainage ditch was laid out, the expenses involved in any future lowering of the culvert pursuant to s. 88.68 (4) shall be borne by the unit of government in charge of maintenance of the highway unless the highway authority in charge of the installation was misled by the drainage board as to the proper grade at which to install the culvert. This section applies only to work done after January 1, 1965.