First about your picture, even though it's a rough draft, I need to point out that you put two 3 to 8 decoders, one used as a 8 to 3 priority encoder (I think), and hooked them up with a single wire on their Z. The idea of the decoder, of course, is having 3 inputs A, B and C, and the binary code will determine which output is enabled. As such the priority encoder turns 8 inputs into 3 wires, A, B and C.
Unfortunately you cannot encode 14 channels into 3 wires.
3 bits allow the numbers:
That's 0 through 7 in binary code. That's only 8 options.
If you want to transmit 14 options over 3 or fewer wires you will need to implement a serial communications protocol, or have multiple levels on a single wire, such as 0V, -5V and +5V. With three distinctive states per wire you can encode 3*3*3 = 27 different states on a 3 wire system. There are, to my knowledge, no standard chips that can do that easily for you. (Tri-state is something completely different, before you ask, since your decoders seem to have that, Tri-state just means you can disable the outputs so they don't interfere with other things when you don't want them to).
With 3 wires you can use different serial protocols. If the system has one common ground, you can use the three wires to use any of the following protocols:
- I2C / SMBus
- RS232 or RS232-TTL
There are more, but these are the most useable with tutorials from the internet. But you will need intelligence that you program to take your 14 inputs and encode them into a datastream, then on the other side decodes them and makes them into outputs as you desire. Doing that will be a whole big step further than you are at this point.
If there is only 3 wires in total, you need to carry the ground over one, and you will not be able to use SPI. If you go a long distance, I2C is probably not a great option, for reasons better explained if you get to that.
One other option, is to multiplex two encoders over 3 wires, but you'll need a protocol around it with some form of synchronisation, to determine when you send the first 3 bits and when the second 3 bits, and that will again require some pre-programmed intelligence.