I agree with Tommy and Bob, looks like water in the oil. Add a little air, and the added volume in the tank along with the design of the filler neck and you start pushing stuff up the filler neck. The filler neck on my HW-03 protruded several inches down into the tank. If the fluid level gets up to the bottom of the filler pipe, as the fluid expands when warm, it traps air in the tank above the filler neck which will force fluid right up the neck as it gets warm. You start adding air to the system, the air adds pressure to the airspace in the tank top and it happens even faster. Somewhere on the top of the tank should be a vertical pipe with a bolt in the top. That is the oil level dipstick. If you remove that bolt/dipstick, it should stop leaking immediately as the air will then have somewhere else to go and won't build pressure to force fluid out the filler.
That was the first mod I did to my BH, I pitched that dipstick and put an inline filter with a short length of hose slid over that dipstick port, and turned it into the tank vent. I then put screws and sealant into the two vent holes in the filler cap and sealed it permanently. I used the filler neck protrusion into the tank to gauge tank oil level...
For your issue, I would drain ALL the fluid out of the tank. If you have compressed air, disconnect the pump outlet hose and shoot compressed air up to the valve to try and get as much of the contaminated fluid out as possible and back to the tank. Unbolt the hose from the suction strainer and pump inlet and inspect the o-ring face seal washers. They are probably a bonded washer, metal or composite and rubber for debris and damage. Also note how tight they are when you remove them. On the pump suction port, it is probably an adapter bolted to the side of the aluminum pump body. Unbolt it and inspect the O-ring in there, also make sure it is snug when putting it back. Don't overtighten as you are screwing into aluminum. On the tank, remove the 3 bolts that hold the suction strainer to the tank and check/clean the filter. While it is off, reach in and wipe out the tank bottom to get as much water out as possible. Re-assemble all teh parts and refill with clean hydraulic oil(AW-32 or equivelent). Run the machine and see if you still have air issues. If so, either one of the suction fittings are leaking, or the pump has a seal issue and is sucking air in the pump. There is of course still contaminated oil in the cylinders which will mix with the fresh oil. A second oil change may be needed to get the most of the water out. Keep the vent covered and sealed when the BH is not in use. A rubber glove and rubber band will work well to seal the filler neck/vents when not in use.
You need to find a gauge and metric adapter to reset the reliefe valve pressure since you adjusted it. Set incorrectly you can break/blow up hydraulic components from excessive pressure.
Good luck