Couldn't you just generate lift with a long body? Maybe a little broader than a normal plane.
As a design enhancement, we would need a heavier bottom, so the plane doesn't flips to a side.
Yes you can, these are called lifting bodies, they are not very efficient and require a lot of speed before they generate enough lift to stay aloft, requiring a long runway.
In 1983 a F-15 fighter lost a wing in a mid air collision and was able to land safely due in part by the main body being able to generate enough lift for the plane to stay controllable.
They are only really useful for supersonic flight where normal wings create too much drag
There are indeed lifting bodies which were able to fly without wings. But wings are much better at creating lift than a bulky fuselage. The space shuttle was developed based on testing lifting bodies, which allows it to have fairly small wings.
What you are describing sounds a bit like the blended-wing-body (BWB), which smoothly integrates the fuselage with the wing. Sort of like a commercial version of the B-2 flying wing design.
This is certainly still in the concept phase. Boeing has flown a scale model to test the concept, and it has performed well. Aside from being more efficient than traditional designs, it can also produce much less noise if the engines are positioned above the fuselage.
We have about 100 years of development in the traditional airplane design, which contributes to the efficiency and safety that we are able to achieve right now. Going with a BWB design alters so many of the standard design features that this presents a very radical change. When the benefits start to outweigh the costs of moving to this design, we may start to see more planes like this.