My fastest time is a 39.6** after 2 tries. Being an autocross driver myself, here are my tips. This single license test is one of my favorite parts of the game!
Be SLOW, as in don't overshoot corners. Instead, keep the car as close to the cones as possible. And in order to do this, you have to be patient with the throttle. It helps to use the hood camera view. I never go past 2nd gear. Setup for the corners so that you sacrifice speed in a previous corner so that you can take the next corner better. This is very helpful in the middle section when you go around the 'boxes'. Use little, controlled steering inputs to reduce amount of body roll especially in the slalom part.