Lavender Thyme

How high does Thymus thracicus grow?? I dug out steps on the hillside in back of my house and put railroad ties down. In back of each of the 6 ties is a 9 inch X 6 feet planter strip, that I would like to plant with thyme. I thought about creeping or woolly thyme, but saw the lavender thyme and thought this sounded beautiful.

Lavender thyme gets 10 to 15 centimeters tall which means it gets about twice or three times as tall as either creeping thyme or woolly thyme.