There should be two separate grounds on the L70. If the power cable is two wire cable, change it to three wire cable, and connect the ground wire of this three wire cable to motor chassis AND under side of top plate. That takes care of power ground.
Your signal ground originates from inside the tone arm tube, so you'll have five tiny wires coming out from the tonearm base and terminated on a tag block on the top of top plate. You can see it if you remove the platter. The right channel are red (+) and green (-), left are white (+) and blue (-). The fifth wire is signal ground, and it must be connected to the ground terminal of the phono preamp.
Make sure that the signal wires from TT to phono preamp/amp is NOT routed close to other equipment like line level preamp or power amp or CD player. It should be as far away as possible from the transformer of the above mentioned devices.