Use a rope for this hybrid movement, which is part upright row, part face-pull. Do 5 sets of 20 reps and rest 3 minutes between sets.
Instead of standing upright, lean back a bit and use the weight stack as a counter balance. With the rope at the lowest point on the pulley, you'll then pull up to your face and chin area as you pull your hands apart. The entire shoulder complex is going to get hit here.
Those guys who think planks and Bosu Ball triceps kickbacks are giving their core a good workout are poor, pathetic slobs. If you really want to work the core, you've got to raise the weight over your head.