  We extract light curves for 4554 objects with $9<G<19$ in the K2 superstamp
observations of the globular cluster M4, including 3784 cluster members, and
search for variability. Among cluster member objects, we detect 66 variables,
of which 52 are new discoveries. Among objects not belonging to the cluster, we
detect 24 variables, of which 20 are new discoveries. We additionally discover
57 cluster-member suspected variables, 10 cluster-non-member suspected
variables, and four variables with ambiguous cluster membership. Our light
curves reach sub-millimagnitude precision for the cluster horizontal branch,
permitting us to detect asteroseismic activity in six horizontal branch stars
outside the instability strip and one inside the strip but with only ~1 mmag
amplitude variability. 19 additional stars along the red giant branch also have
detected asteroseismic variability. Several eclipsing binaries are found in the
cluster, including a 4.6-day detached eclipsing binary and an EW-class
eclipsing binary, as well as an EW with uncertain cluster membership and three
other candidate EWs. A 22-day detached eclipsing binary is also found outside
the cluster. We identify a candidate X-ray binary that is a cluster member with
quiescent and periodic ~20 mmag optical variability. We also obtain
high-precision light curves for ten of the previously known RR Lyrae variables
in the cluster and identify one as a candidate Blazhko variable with a Blazhko
period in excess of 78 days. We make our light curves publicly available.
