Command-line implementation of Mastermind
Simple things you can improve:


12 is a magic number in your code, you can move it to a constant.
I think TURNS.times do |turn| ... is better than the while loop because you don't have to keep track of the counter.
When you're passing a simple space (" ") to the method split you can just call split instead, without passing any argument.
When the block has multiple lines it is a good practice to use do and end instead of brackets.
I think you can use the select method and assign the result directly to the correct_colors variable.
I think it would be better to call Game.new.start_game instead of Game.new, for me, it isn't intuitive that the game will begin just by instantiating the Game class.
You can make some methods private because you are not calling them on the instance.