This is a "million dollar question." Someone has given you a very specific task that has probably been tried before and there are no published papers with an answer. a) maybe someone has a way to do this and it is not published due to trade secrets, etc. b) maybe it has been tried and someone has given up.
For making high surface are graphene, I would start with the Worsley paper. link: http://pubs.rsc.org/en/content/articlelanding/2012/cc/c2cc33979j#!divAbstract This gives a very clear process for making a area high srfacegraphene aerogel, a supercritical dried will be needed. How to include the MnO2? That is the tricky part.
If you are looking for addition papers, I would start by searching US patents for graphene + Mn02. Good luck!
Look references for metal oxide decoration onto grahene oxide and figure out which precursor you would need for manganese oxide. I have to say that many questions in RG are as specific as this one and can be solve by an adequate search analysiis strategy. See what you can figure out form similar systems