QUICK TIPS: Be Engaged!!
If you feel you are fighting the false perception that you aren't an active participant and that you don't care about your job, you should try to take every opportunity to show that you are engaged at work. Engagement means many things, including coming up with more efficient ways of doing a task, thinking of ideas and sharing them with higher-ups, being proactive and not waiting to be asked to do things that are within your authority to act on, speaking up if you notice problems or issues that impact productivity, etc.
One of my favorite ways of showing engagement is coming up with and sharing new ideas. This shows an interest in the business. It shows that you are thinking in a positive fashion and are solution oriented.
I will say this...If you make suggestions, come up with new processes, or act proactively and successfully to address an issue, you should document everything in writing. Documentation can be used to show that you've been an active participant at work, that you've come up with and shared ideas, that you've taken ownership of addressing certain issues and that you are committed to positively contributing to the success of the company.
Try to be as engaged as possible at work. Even if your ideas aren't always or ever adapated at work, the one thing you can't be accused of is not trying to contribute to a more successful and positive environment.