Is there a relay package which can be triggered by a numeric coded pulse?
I know this would be a fairly simple logic circuit to make, ... but I'm wondering if such a product already exists, ...


It probably doesn't exist.
When you have the luxury of one or more wires you'd typically use a versatile or robust solution.
One which offers more than just unsolicited command shouting, such as I2C.
One that isn't as susceptible to noise as a single ended wire. Such as RS-485.
One which layer 2 protocol contains data integrity checks, such as CAN-bus or MODBUS-RTU.   

Shouting 01110111 over a wire won't be a suitable solution in the industry for obvious reasons.
It is however widely used in cheap 433 MHz remote control sockets. A set of dip switches then configures the numbers it will listen to.