"If you want to code, code.
If you want to draw, draw."
And if you want to design games, design games.
Design board games. Write an RPG system and give it away. Design a CCG, print it out using a POD business-card printer. Playtest the things, am-publish them. Just get on with it. Bloody hell, this forum is constantly full of people whining that they don't have the resources to do games when the world is awash with print on demand houses and games components sellers. Design wargames -- that's how I got one of my games development gigs. I can code AND I understand how to simulate tank combat.
Games are games -- understanding what makes a game fun and how people interact with games and with each other while playing them is the experience you need. Want people to let you see what you can do with their $10M-a-month dev team? Might be worth demonstrating you can design a game with $50 of random components first. Because the guys who already ARE running those teams definitely can; Molyneux, to pick an example, apparently designed Populous as a boardgame to start with (using Lego for the modifiable landscape).
What better way to get hired than being able to send the company one of your games that you know is fun and letting them find out that you can make things people want to play. And if you can't do that, why would someone give you millions of dollars a month?
Seriously -- if you can't look a pile of parts and figure out how to make a game from it, you're not a game designer. Because games designers don't NEED a bunch of coders and artists to make something that entertains people. The medium is not the skill. And if you can't afford marble yet, sculpt in clay until you can.