  Evidence is presented for the electroweak (EW) production of two jets (jj) in
association with two Z bosons and constraints on anomalous quartic gauge
couplings are set. The analysis is based on a data sample of proton-proton
collisions at $\sqrt{s} = $ 13 TeV collected with the CMS detector in
2016-2018, and corresponding to an integrated luminosity of 137 fb$^{-1}$. The
search is performed in the fully leptonic final state ZZ $\to$
$\ell\ell\ell'\ell'$, where $\ell,\ell' = $ e, $\mu$. The EW production of two
jets in association with two Z bosons is measured with an observed (expected)
significance of 4.0 (3.5) standard deviations. The cross sections for the EW
production are measured in three fiducial volumes and the result is
$\sigma_{\mathrm{EW}}$(pp $\to$ ZZjj $\to$ $\ell\ell\ell'\ell'$jj) = 0.33
$^{+0.11}_{-0.10}$ (stat) $^{+0.04}_{-0.03}$ (syst) fb in the most inclusive
volume, in agreement with the standard model prediction of 0.275 $\pm$ 0.021
fb. Measurements of total cross sections for jj production in association with
two Z bosons are also reported. Limits on anomalous quartic gauge couplings are
derived in terms of the effective field theory operators T0, T1, T2, T8, and
T9.
