Might be going to far in explaining this but if you look at the radio signal it starts with a long off period (this is the sync pulse) and then a bunch of on/off periods to denote the zero/one bits. Luckily the only difference between a one bit (equal on/off period) and a zero bit (on for half the off period) is the on time so you can use code to measure the time between successive rising/falling edges you can usually decode the signal.
Attached is code I wrote for decoding my own sensor, it is not the same as yours but the principle is the same so hopefully you can enter the bit count, needed timings to match your signal and maybe invert the logic to decode it.
WeatherRF_me.ino (6.51 KB)