The top hole is indeed used for the washer drain.
The lower pipe is used to drain a washing machine pan.
If the washer leaks this pipe allows the water to drain away safely, instead of flooding the laundry area.
I don't quite follow your description, the standpipe configuration might be part of the problem. The gurgling toilet indicates a venting problem, I don't think it would contribute to overflowing, but it is a problem. As mentioned, a photo or diagram is needed for better assessment. My intent is to describe a proper washer installation and address how the height plays into it.
There are all sorts of variations for pipe configurations, this one is very typical. The washer drain ties into the 4" horizontal pipe with a vertical 4x4x2 LTTY (long turn tee-wye). It can be installed flat to gain some vertical, at the cost of an extra ell that introduces a potential clog point.
From the LTTY is a vertical 2" pipe as short as possible before connecting to a 2" sanitary tee. A 2" vertical pipe continues up to tie into the venting system. The vent could be reduced to 1.5" if need be. The side inlet of the santee takes a 2" horizontal (2% slope actually) trap arm. There is a length limit, but it's rather long, it's best to keep it rather short. The trap arm connects to a 2" trap assembly. The trap inlet accepts a 2" vertical stand pipe.
The stand pipe must be a minimum 18" high, straight up, no bends. You cannot connect a washer discharge directly to a closed drain system. There must be an overflow provision such as an open stand pipe. I prefer to see about a 24" stand pipe, but 18" is a code requirement.
This gives you about a 24-30 inch tall stand pipe/trap assembly on top of the 48" height of the main drain, so a total 6-6.5 feet off the floor. Washers have a limit of how high they can pump discharge water. The installation instructions should tell you this somewhere. If not, you may need to contact the manufacturer. If your washer can pump up to the top of the stand pipe while sitting on the floor, you're all set. If not, you will need a platform that raises the washer to within the allowable discharge height.
If you still get overflowing with a proper standpipe-trap configuration, then the main line remains obstructed somewhere.
Best Answer
I would not extend the drain hose that is supplied with the machine.
However, what I have done in the past is to put a stand pipe closer to the machine with a U trap to prevent the smells coming back up.
I did that with 2" pipe which solved the problem and never caused any back up for the machine.
The 60" is usually taken as horizontal distance but the man ual will make that clear.