Networking Multiple Arduinos -- Is It "Rocket Science?"
The best solution would be to use an RS485 adapter connected to each Arduino via serial port. This is a tried and true solution that is perfect for a setup like this and only costs a few bucks of extra hardware per node.
If you can't use additional hardware, you can also create a poor-man's current loop system like RS485 using normal Arduino pins since they are capable of sourcing and sinking 20mA.
With either of these solutions, you can send however much data as you want as long as you have some kind of minimal protocol to serialize it into a sequence of bits on the wire. To send 12 bits, you might just define a start condition as an idle &quot;0&quot; on the wire for a certain period of time, followed by a &quot;1&quot; start bit, followed by you 12 data bits, followed  maybe a parity bit or a checksum, and completed by a &quot;1&quot; stop bit.
Check out how, say RS232 or RS485 serialize bits to get an idea of how this works. If you end up using hardware that only supports sending data in 8 bit chunks, then you could, say, send two bytes per data &quot;packet&quot; where each byte has 6 bits of your data, plus one bit that indicates if ths byte is the first group of 6 bits or the second group, and then one bit of parity for error checking.