Do I need an extremal filter

Hi, I was wondering if I need a better filter for my tank of its this enough?
I've got Juwel Rio 125 litre tank with Bioflow 3 filter which pumps 600l/hour and had volume of 3 litres.
There are 2 swordtails, 16 neons, 10 cardinal and 3 black tetras. There's also 12 plants.
The water doesn't sink and the parameters are very good with no ammonia, NO2 and NO3 between 0,05- 0.75ppm. The tank is new, fish were bought in the beginning of June.
However, I see tiny dust like particles in the water and when I do WCH once a week filter floss appears very dirty, like completely covered in mud. It's that normal? I think this mud comes from the substrate - plant substrate and gravel. I had to wash it for 45min before placing into tank because it was extremely dirty and dusty. It still wasn't completely clean when I gave up because I physically couldn't continue washing it anymore. It was a store bought aquarium gravel but I'm not sure where they got it from.
So my question is would it help to get an external filter - I'm thinking of Eheim, or is my current filter enough?

Edit of the title : I'm on my mobile and it changed the word external to extremal. I don't know how to correct it now, so sorry for the typo

 

Recommended filtration is 8-10x the tank size so I would get another filter that turns over another 600 l/hour. That might be why your media is getting dirty faster.

 

Thanks. I wasn't sure about it. The filter is quite costly and I would rather not invest if not necessary. It also doesn't look good with the hoses going out of the tank. On the other hand I don't like the state of the medium after a week.
So I will consider buying it.
If anyone has further suggestions I'll be grateful. I want to buy Eheim profesionel 4 because it looks very good and I've found a good price in one shop.

 

Are you sure it's substrate and not extra food? How much and how often do you feed?

 

I feed 2x day what they eat in 1-2mjnutes.
There're some granules in the filter (a few grains) but the rest of the mud is same texture and colour as dirt that came out of gravel when I was washing it the first time. It also resembles Tetra potting soil that is below the gravel. It's kind of hard to say which one it is.

 

OK, another question.
If I buy a new external filter can I still use the heater that's inside the original internal filter? It has its own cable and is plugged separately.
Is it safe to turn it on and leave it in the old filter box if the water wouldn't flow? Or do I need to buy an extremal filter with thermostat which is 100€ more expensive?