- Sound pressure level (SPL) depends on the loudness of the sound and the distance between the sound and the microphone in the meter. Further away = lower SPL.
- The volume depends on the power supply. To get the loudest output, you need to use the highest power supply voltage the chip is rated for.
- The volume depends on the speaker. A tiny little speaker won't be as loud as a somewhat bigger one. Too big is bad as well, though. You won't want to try to drive a 100 watt sub-woofer with an LM386. The speaker efficiency plays a part as well. A low efficiency speaker won't be as loud as a more efficient speaker.
- The volume depends on the enclosure. A speaker in free air has a sort of "acoustic short circuit" - the sound waves generated by the front and the back of the speaker cancel each other to some extent and reduce the volume.
- The volume depends on the input signal. The higher the input level, the louder the output volume - up to a point. If the input is too high, then it would take more than the available voltage to produce the output signal. The amplifier clips, and sounds horrible - and doesn't get any louder.
56dBA might be a reasonable volume for your setup. There's no way to tell from here without details you didn't provide.
The LM386 is not a high power amplifier. Wikipedia says that depending on exactly which version of the LM386 you use (and the powersupply voltage and speaker impedance) the maximum power output ranges from 0.3 watts to 1 watt of power output. No matter how good (or bad) your speaker is, you aren't going to get window rattling, bone jarring bass out of the LM386.