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The Planck scale, where quantum gravity should have directly observable consequences, is ~10^18 GeV. The world's most powerful collider to date, the LHC, reaches a collision energy of ~10^4 GeV, not far from the theoretical maximum attainable by a ring of its size [1].

If you wanted to scale up the LHC by an energy factor 10^14, you would have to deal with the energy loss caused by synchrotron radiation (charged particles going around a ring are constantly accelerating, so constantly emitting electromagnetic radiation) which is ~E^4/R per turn [2]. To keep the same energy loss as at the LHC and pay an electricity bill which is only 10^14 times larger, you would therefore need to grow the radius R by a factor ~ 10^14^4 = 10^56.

The LHC radius is 4.5 km, so let's go with R = 10^56 km. That's 10^43 light years. For comparison, the radius of the observable universe is ~10^10 light years.

[1] http://www.physics.princeton.edu/~mcdonald/examples/lep.pdf

[2] https://arxiv.org/abs/1504.01627

[3] https://en.wikipedia.org/wiki/Observable_universe#Size




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