Sure! Here's the code for a simple game that meets your requirements:
To play the game, just open this HTML file in a web browser, and it will display a canvas where you can tap/click. Every time you tap, the level increases, and when you reach level 15, the square turns into a warrior square.
The square starts at size 20 and remains the same size as you level up. The level is displayed at the top left corner of the canvas.