From results doing a search of Tennessee Union soldiers at the National Park Service Civil War Soldiers & Sailors System...

http://www.itd.nps.gov/cwss/

Gothard, Elias
1st Battalion, Tennessee Light Artillery

Gothard, Joel
6th Regiment, Tennessee Mounted Infantry

Gothard, Larkin J.
6th Regiment, Tennessee Mounted Infantry

Gothard, William
5th Regiment, Tennessee Cavalry

Gothard, William B.
6th Regiment, Tennessee Mounted Infantry

I didn't see any results for the spelling "Gotherd". You can always check other states to see if he served from a diiferent state.