Hi zang! Yes you are on the right track.
I went through this last year with an Acurite rain sensor (model 00899). It was very interesting and not too terribly difficult. I will try to find my notes later, but....
The four rather longer pulses at the beginning and three "repeats" sounds about the same as what I saw. And the longer/shorter pulses indeed were simply 1's and 0's, with no other decoding necessary (e.g. "Manchester" or such).
If I were you I would begin by capturing the data as you have by hand. Transcribe the pulses as bits where long-low/short-high is 0 and short-low/long-high is 1 (it could turn out to be opposite but that's how it was in my case). And of course record all the current readings from the base unit that go along with it. Wait for something to change, and repeat.
Something like this
current values --- bits
40,30,21,32 - 00111000 11001110 00111000 11001110 00111000 11001110 00111000 11001110 00111000 11001110
41,32,20,31 - 11001110 00111000 11001110 00111000 11001110 00111000 11001110 00111000 11001110 00111000
40,30,21,32 - 00111000 11001110 00111000 11001110 00111000 11001110 00111000 11001110 00111000 11001110
43,32,20,31 - 11001110 00111000 11001110 00111000 11001110 00111000 11001110 00111000 11001110 00111000
You probably already know this-- but my point is you can probably succeed, and I or others can probably help with the analysis if you need..
How many bits/pulses are you seeing in each of the three repeating groups?
And the coding-- how is your Arduino programming experience?
Cheers,
John