A subdistrict of a drainage district organized under, or made subject to, §§ 14-121-101, 14-121-102, 14-121-104, 14-121-105, 14-121-201 — 14-121-205, 14-121-207, 14-121-301, 14-121-304, 14-121-305, 14-121-307, 14-121-310, 14-121-311, 14-121-313, 14-121-401 — 14-121-406, 14-121-408, 14-121-411, 14-121-412, 14-121-422 — 14-121-432, 14-121-440 — 14-121-442, 14-121-802 — 14-121-805, and 14-121-808 may reconstruct, repair, enlarge, straighten, extend, and improve ditches, drains, levees, sluiceways, flood gates, and any and all other construction work of the original district for the reclamation of wet and overflowed land, as a part of the system of improvements of the subdistrict, provided the work shall be done at the expense of the subdistrict.