It doesn't just look like a speed walk, it IS a speed walk. As long as both feet are never off the ground at the same time, it's walking. To make it a run, there has to be a point where both feet are in the air at the same time, and for that to happen you need to give him a bit more bounce. Like Blick said, vertical movement.
I also think you've tried making him lean forward to make it look speedier, no? Don't be afraid to overdo it. If you want a real power dash, you could have him almost diagonal as long as you make him push off the ground with enough force.
But for now, focus on vertical movement. Actually, how many frames have you got there? Six? I'd recommend you tack on two more to get rid of the jerkiness, too.