The Code indicates it was made on 27 October, 2011. The manufacturing plant code, 51, is not actually a manufacturing plant, it is a facility located at B&S head office and is described as "TBS", whatever that means. I suspect your engine was actually made in Plant 28 in Chongqing. Briggs' manufacture of small side-valve engines in the US was pretty much phased out by 2011. This involved closure of a number of US plants.
The numbers are not clearly stamped. I think that is 9T502-3152-H1. If so, here is the illustrated parts list for it:
http://bsintek.basco.com/BriggsDocumentDisplay/18kvuIXSnfBhU7y.pdfHere is some information on carburetor parts from the Outdoorking on-line store.
https://www.outdoorking-forum.com.au/index.php?main_page=index&cPath=193_195_203If you can't find what you want, I suggest you send a Private Message to Bruce, the site owner - he'll be able to help.