Looks like your ancestor enlisted in what was known at the time as the 29th (Pleasant's) Arkansas Infantry before it became the 37th after Dec 1862. He was detailed to serve as an artillerist May-June 1862, but died at Camp Hope, Arkansas on October 6, 1862. Many men died at Camp Hope/Camp Nelson, all around Austin, Arkansas in the fall of 1862. A huge Confederate cemetery there with almost all having unknown headstones from VA. Undoubtedly your ancestor rests in one of these hundreds of unknown graves. Here is the link to the Encyclopedia of Arkansas History for the cemetery...

http://www.encyclopediaofarkansas.net/encyclopedia/entry-detail.aspx?entryID=4275

For info on what the regiment went on to do, here is entry...
http://www.encyclopediaofarkansas.net/encyclopedia/entry-detail.aspx?entryID=12211