they were chambered in 30-30 so, perhaps you should try that first.
Your serial number indicates that your Marlin model 336W was made in the year 2009.
2005.
All that I can say is that the marlin model 336W/30AW were made during 1983-2007.Most of these were sold thru Wal-Mart.
WAL-MART
1978
2000
1977
Contact Marlin via their website and request an owner's manual
Your serial number provided is not complete.Please provide the whole number on the tang or receiver to receive an answer to your question.
The W means walnut. AC is walnut stained hardwood.
In the Marlin 336A, the "A" designates the model variant of the Marlin 336 lever-action rifle. The "A" typically indicates features such as a standard barrel length and a specific type of finish or stock configuration, distinguishing it from other variants like the 336C or 336W. The Marlin 336 series is known for its reliability and versatility, often used for hunting and sport shooting.
I found the complete breakdown on google, I googled marlin 36, as i have a marlin 36a, and one of the first few choices were for the 336, It will be in the gun digest book of firearms, firearms assembly/disassembly, part IV centerfire rifles. 2nd edition.