Assuming you're using the same programming language, you'd need the the same amount of code. Why? You're changing the nature data is stored on a chip, not the programming language. The advantage of having 8 states would be to increase the amount of data that can be stored on a chip of the same size.
Example (correct me if I'm wrong):
Let's say you want to store the number 8. In binary code, you'd need 4 "storage spaces" (e.g. 4 surface area units) to store 1,0,0,0 because that's number 8 in binary. When there are 8 states, you'd need 1 storage space to store the number 8. However, if you need to store two pieces of code, "8" and "8" (not the number eighty-eight). You'd need 4 storage spaces for the first "8", another 4 for the other when data is stored in binary states - a total of 8 storage spaces. When there are 8 states, you'd need only 1 storage space for the first 8, and another 1 to store the other 8, hence significantly reducing the amount of storage spaces needed. However, when writing the code on a piece of paper, you'd write 8,8 on either the binary or the 8 states system. They'll just be stored differently.
Processing speed will definitely be increased for the 8 states system (as opposed to the binary system) if the chips for either system can be read or written (i.e. switched to different states) at the same speed, but that's only an "if." The increased speed comes from the fact that there would be less "storage spaces" (e.g. chip surface area) to process.