It's already confirmed 0.00037056 BTC fee is already enough, sometimes when i send transactions, my transaction fee is 0.0000x BTC or most commonly 0.00000x BTC , I always use different Transaction Broadcasters and Confirm Tx and AntPools Transaction Accelerator,) Check Zepher's Thread =
https://bitcointalk.org/index.php?topic=2510862), which helps a lot though some of my transaction take almost 3 hours before the confirmation because of the low fee.