Vidqun - DNA is not information in the same sense of the word that this sentence is information.
There is no sender or receiver. It is just a complex dance of electrons.
How do you think DNA developed?
Briefly - nucleotides formed in hydrothermal vents.
The acetyl CoA pathway (to be exact a prebiotic equivalent) generated small reactive organic molecules from CO2 and H2 via a few short steps that generated enough energy to drive the formation of nucleotides and their polymerisation into long chains.
These steps were catalysed by inorganic minerals that transferred electrons on to CO2 to form reactive acetyl groups. If you would like to understand the details and read about the work being done in labs to investigate this process get a copy of "The Vital Question" by Nick Lane.