  This letter reports the unexpectedly strong electron-phonon coupling (EPC)
and the highest $T_c$ record ($\approx$ 38 K) among the MXenes revealed in the
2H-Mo$_2$N under biaxial stress. At first, its excellent mechanical properties
are demonstrated with ideal strength of 37 GPa and elastic modulus of 438 GPa.
Subsequently, EPC and corresponding $T_c$ are elucidated upon the dynamically
stable range of strain. For strain-free 2H-Mo$_2$N, the EPC constant
($\lambda$) and $T_c$ are 1.3 and 22.7 K, respectively. This $T_c$ is higher
than those of 2H-Mo$_2$C (4.3 K), 1T-Mo$_2$N (16.8 K), and other pristine
MXenes. The material exhibits remarkable enhancement in $\lambda$ and $T_c$
when subject to compressive and tensile stresses. The obvious strong EPC with
$\lambda$ over 2.0 occurs at strains of -4%, -2.5%, and 5%, yielding $T_c$s of
37.8, 35.4, and 28.9 K, respectively. Our findings suggest that the
strain-dependent feature and energy levels of electronic bands play an
essential role in enhancing EPC. Moreover, the stronger EPC in Mo$_2$N compared
with Mo$_2$C is clarified based on lattice vibrations. Therefore, this work
paves a practical way for designing 2D superconducting materials using tuning
atomic recipes and strain-dependent engineering.
