I couldn't find a clip with this particular phrase but this seems close enough: https://youtu.be/YT1vXXMsYak?t=613
Richard Dawkins himself admits "there is a lot wrong with that as a demonstration of Darwinian natural selection." However, Philip, I believe you misunderstood a key part of the experiment. Each letter doesn't stop when it's the correct one. Rather, starting from a random phrase, the computer breeds 50 new phrases, each with a tiny mutation. It then picks the phrase from those 50 that most closely resembles the target and repeats the process over and over. This crudely mimicks natural selection: you can imagine that the correct letters are traits favored by the environment.
The target phrase is reached in 158 "generations".