We report a comprehensive study on low-lying parity doublet states of 224Rn by mixing both quadrupole- and octupole-shaped configurations in multireference covariant density functional theory, in which broken symmetries in configurations are restored using projection techniques. The low-lying energy spectrum is reasonably reproduced when the shape fluctuations in both the quadrupole and octupole shapes are considered. Electric octupole transition strength in 224Rn is found to be $$B(E3; 3^-_1 \rightarrow 0^+_1)=43$$
B
(
E
3
;
3
1
-
→
0
1
+
)
=
43
W.u., comparable to that in 224Ra, whose data are 42(3) W.u.. Our results indicate that 224Rn shares similar low-energy structure with 224Ra despite the excitation energy of first $$3^-$$
3
-
state of the former nucleus is higher than that of the latter. This study suggests 224Rn is a candidate for the search for permanent electric dipole moment.