The image of the actual marriage certificate is online but does not provide any information on parentage of either party. Maybe if you could locate the 1830 census for Washington, GA you might find other Hodges?
Georgia, County Marriages, 1785-1950
https://familysearch.org/pal:/MM9.3.1/TH-1942-25515-18292-86?cc=1927197&wc=M9S4-23K:1979055403
Name: Elbert Hodges
Marriage 24 Dec 1828 Laurens, Georgia
Spouse: Silance Culpepper
Film Number: 410104
Digital Folder Number: 5191021
Image Number: 434
U S Census, 1830 Washington, Georgia
Citing this Record "United States Census, 1830," index and images, FamilySearch (https://familysearch.org/pal:/MM9.1.1/XHGB-GGH
Name: Elbert Hodges
Event Place: Not Stated, Washington, Georgia
Page Number: 275
Affiliate Publication Number: M19
Affiliate Film Number: 21
GS Film number: 0007041
Digital Folder Number: 004409523
Image Number: 00548