From nothing, to detectable, to lethal, to big boom?
My intuition would be "detectable" but I don't know enough to do the maths.
And by the way, I am using the mass-energy, not proper mass, because the question is crazy enough not to even consider what would be the mass of a neutrino.
The MFP of a 120 PeV neutrino in lead would be something like 10 kilometers, I think.
The probability of interaction of neutrinos with matter increases with the energy. I've asked o1 to estimate the mean free path of a 120 PeV neutrino in water and it came up with 1000km. So let's say, conservatively, that 10^-7 of the total energy gets deposited in your body when the beam goes through. The mass equivalent of a ping pong ball is about 2.5x10^14 J, which gives us 2.5x10^7 J total, or about 6kg TNT equivalent. This is only an order-of-magnitude estimate, but it would definitely not be healthy.
So BIG boom.
Since the velocity is so close to the speed of light, you can think of this like the energy released by annihilating a ping pong ball made of antimatter.
Edit: Commenter asked what would happen if they "hit", so I'm assuming a hypothetical 100% collision. But yes to stop 1/e of a neutrino beam with normal matter, you'd need a light year of lead.