A noise gate cannot reduce the noise of your amp. Basically the theoretical best you can manage is getting to the noise level with nothing plugged in (strictly speaking, the noise level when plugging in a plug that has been short-circuited, but that should usually be similar).
If it's the amp producing the noise, anything that you put before the amp will produce at least as much noise as leaving the amp without input.
If the amp has an "effect loop" out/input, putting your noise gate there might be effective. If you have a separate over-drive brick, it needs to get wired before any noise gate to be effective: overdrives tend to work as mostly linear amplifiers at high gain setting for small signals, so they are likely to produce/amplify noise.
Note that a noise gate can in some situations act more distracting than constant noise. You just have to try.