Well, a supernova throws off a lot of mass, but gravitational waves require both mass and acceleration; it’s not enough if there is just a shift of mass. In a supernova, the mass ejected would be decelerating, unless there was some other nearby gravitational source to accelerate it, so I don’t think it could produce gravitational waves.
When the nuclear fires go out the core collapses at nearly the speed of light and can form a blackhole in less than a second. The next generation gravitational interferometers will be sensitive enough to detect these.