Limp it to the tire shop NOW.
The problem isn't the gouge, it's the bulge to the left of it. This is a broken steel belt. This tire could catastrophically fail on you at any time, meaning instantly tear itself apart, and cause severe handling problems when it does. It will be a challenge to keep the car from hitting other traffic, roadside objects, pedestrians, bicyclists or even just keep it from flipping over -- depending on how much kinetic energy you have at the time.
Kinetic energy is a function of speed squared.
So I recommend you just limp it to a nearby tire shop, and here's the important part - keep your speed down to 20 mph - 25 tops. You will still need to be on your toes because the car could lurch off in an unexpected direction at any time. However at this low speed, your kinetic energy is quite low, so the other 3 tires should have enough authority to keep the vehicle controllable, and there's no real chance of rolling the car over. And events will unfold slowly enough that you should be able to react to them.
Now, a couple things are important about replacement tires.
First and foremost, your best rubber needs to be on the rear axle regardless of drive system. Period. You don't want to find out what happens when it's not.
Second, it's best that on the drive axle(s), the tires be of roughly equal diameter/wear. If they're not, the differential will have to work extra hard. It's not a deal-killer, but better to avoid it. Here, used tires can be a salvation, because they can let you match the other tire that is worn, instead of having to spend to replace 2 tires.