I can hear a colored noise and it remains even after I turn down the volume of my guitar.

Sometimes this kind of noise becomes louder if the gain level is high, depends on settings of your selected an amplifier or effects.
You can reduce this noise with the “Noise Reduction”, however please note that too much noise reduction causes unnatural sound.
And, turn down volume nob, if a microphone is not used.

(3/7/2013)