The quadratic function $g$ models the depth, in meters, below the surface of the water of a seal $t$ minutes after the seal entered the water during a dive. The function estimates that the seal reached its maximum depth of $302.4$ meters $6$ minutes after it entered the water and then reached the surface of the water $12$ minutes after it entered the water. Based on the function, what was the estimated depth, to the nearest meter, of the seal $10$ minutes after it entered the water?