(a) Upon the filing of the assessment, the clerk shall give notice of that fact by publication for two (2) weeks in some weekly newspaper issued in each of the counties in which the lands of the district may lie.
(b) The notice shall give a description of the lands assessed and shall state that the owners of the lands, if they desire, may appear before the court on a certain day, naming the day, and present complaints, if they have any, against the assessment of any lands in the district.
(c) The day so named shall be more than ten (10) days after the last publication of the notice.
(d) If no complaint is made as herein provided, the assessment as deposited with the clerk shall be conclusive.
(e) Any owner of real property within the district who perceives himself to be aggrieved by the assessment of benefits or damages or deems that the assessment of any land in the district is inadequate shall present his complaint to the court on the day named in the notice.
(f) The court shall consider the complaint and enter its finding thereon, either confirming the assessment or increasing or diminishing the assessment.
(g) Its findings shall have the force and effect of a judgment, from which an appeal may be taken within thirty (30) days, either by the property owners or by the board of the district.