04 bmw x3 audio wires

Cut the negative speaker wires, insulate the wires that come from the radio.  Ground all 4 of the wires of the harness.  This may be the Medium you are speaking of. 

Do not ground the speaker wires that come from the radio, only the negative wires of the harness.

Yes that is the plan. 

On the speaker wires of the radio, there is signal on both the positive and negative wires.  With both of the signals, it is overdriving the amplifier.  If you ground the negative input wires, this will eliminate half of the power going into the amplifier.    It depends on what is distorting, if the inputs of the amp are being overdriven, this will fix the distortion problem.  If the distortion is being introduced to the amp by the radio, it will not help your distortion problem.  I am banking on the inputs of the amp are being overdriven.     If there is a pop when you change the radio stations after you do this, do not panic.  less than 8 dollars at radio shack and we are done.

It is very critical to have the negative wires of the harness grounded properly.  Any lack of integrity of this ground will produce an audible noise just as you are describing.  With the radio on but volume really low, touch move and tap all of the connections made to the harness' negative wires.  If any of these actions change the static noise, that connection needs to be dealt with.  If those actions do not change the static, you may have to try the 8 dollar Radio Shack repair.  I can not give you a percentage of chance that this will help you but I think it is worth a try.  Purchase 1 or 4 of either of the following.  Larger value is preffered.  All should be the same, they may have only 2 of each in stock.  You may have to hit a couple stores.  http://www.radioshack.com/search/index.jsp?kwCatid=&kw=non%20polarized%20capacitor&origkw=non%20polarized%20capacitor&sr=1  

Take some speaker wire and strip enough insulation off of the wire to use the insulation to slide over the legs of the capacitors.  Cut the radio's positive wire from it's connection point at the harness.  connect the cap in series with that speaker wire.  There is no positive or negative end on the capacitor, you can not connect it backwards.  Try this on one speaker, you will have to put your ear in the speaker to see if it gets rid of the noise.  If it works proceed to the rest of the wires.  That is why I said 1 or 4.  1 because I am not sure it is going to fix this problem.  4 if it is a hassle to get to the radio shack and will cost more in fuel to go back.