Puckering usually occurs because the fabric gets stretched. A walking foot helps because it feeds the top and bottom layers more evenly. However, for me, it's not enough to prevent puckers. Here's what I do.
Before layering, I *heavily* starch the backing fabric. I use a 1:1 solution of Sta-Flo liquid laundry starch, "paint" this on with a large wall painting brush until the fabric is saturated, toss in the dryer, then iron with steam. This stabilizes the backing so it doesn't stretch and get puckers sewn in when I quilt. I spray starch the top before layering.
For layering, I spray baste. Spray basting holds the layers together everywhere (instead of a joining point every 5" with pins), which helps prevent fabric from stretching.
Be careful how you handle the quilt, especially when crossing quilting lines. The tendency is to push and pull the quilt, especially to prevent a pucker when crossing a quilting line, but this only makes everything worse. You want to be sure that there is no drag around the area being quilted. This includes making sure the rest of the quilt isn't hung up on an edge and also making sure that you are not stretching the fabric with your hands as you quilt. *Smoothing* the quilt around the needle is okay; *stretching the fabric around the needle ultimately creates puckers.
Edit: Even now you may be able to reduce puckers by spray starching the top and backing. Lay out the quilt on the floor, spray with starch, allow the layer to dry (a fan on the quilt helps), mist again with spray starch. Do both sides maybe 3 times. This will help stabilize the fabric so it has less of a tendency to stretch while machine quilting.