I'm trying to find where truffle store the compiled code. I'd like to take this bytecode and to deploy it manually with MyEtherWallet
Truffle will save the compiled contract(s) in < project_name >/build/contracts folder.
Note: it is possible to deploy contracts to a network without running an Ethereum full node, via Truffle, by using Infura instead. The details of which are documented on Truffle's website.