  A search for $CP$ violation in the Cabibbo-suppressed $D^0 \rightarrow K^+
K^- \pi^+ \pi^-$ decay mode is performed using an amplitude analysis. The
measurement uses a sample of $pp$ collisions recorded by the LHCb experiment
during 2011 and 2012, corresponding to an integrated luminosity of 3.0
fb$^{-1}$. The $D^0$ mesons are reconstructed from semileptonic $b$-hadron
decays into $D^0\mu^- X$ final states. The selected sample contains more than
160000 signal decays, allowing the most precise amplitude modelling of this
$D^0$ decay to date. The obtained amplitude model is used to perform the search
for $CP$ violation. The result is compatible with $CP$ symmetry, with a
sensitivity ranging from 1% to 15% depending on the amplitude considered.
