This isotope shows up as an inevitable contaminant in Plutonium-239 for nuclear weapons, because it emits neutrons too fast and makes it harder to assemble the critical mass without fizzle.
It is the presence of this contaminant that made implosion-type fission weapon a necessity: Section "Gun-type fission weapons don't work with plutonium".
Wikipedia explains that Pu-240 is formed by Pu-239 Neutron capture:so its presence is inevitable.
About 62% to 73% of the time when 239Pu captures a neutron, it undergoes fission; the remainder of the time, it forms 240Pu.