Your Mustang has a factory amp. It has to be turned on, or bypassed. If you used a harness with one long, flat plug and one small, square plug, then you're feeding the factory amp instead of the speakers with your head unit's output.
There are two options:
1. Make sure the blue/white wire in the long, gray plug is connected to the blue/white wire from your head unit.
2. Dig a little deeper into the head unit cavity. You should find a long, black plug that looks like the twin of the long, gray plug you're using now. If you get a standard Ford harness, you can use it to connect to the black plug and it will automatically bypass your factory amplifier. Then your speaker outputs will be connected directly to the speakers, instead of the factory amp input.