The short answer is "Yes" if it's temporary, for construction, and you can meet the requirements as stated in Chapter 156.222 which say:
(A) Temporary construction structures and uses. The following standards shall apply to all structures used for construction purposes on a development site:
(1) A zoning permit for such structure shall be required, prior to installation.
(2) No temporary structure shall be used as a dwelling unit.
(3) The placement of temporary structures shall be in conformance with the requirements of this chapter.
(4) Temporary structures may only be used for the storage of construction materials, tools, supplies and equipment, for construction management and supervision offices, and for temporary on-site sanitation, solid waste or fuel facilities related to construction activity on the same lot.
(5) Temporary structures shall be removed from the lot within 15 days after an occupancy permit is issued by the city for the permanent structure on such lot, or within 15 days after the expiration of a building permit issued for construction on such lot.
A Zoning Permit must be submitted and approved with the City of Marshall Zoning Administrator as well. Click here to download a Zoning Permit. Click here to download a Dumpster Permit. The cost is $20.00.