Let $S_{k}={\mathbb{F}}_{q}[u_{1},u_{2},\ldots ,u_{k}]/\langle u^{3}_{i}=u_{i},u_{i}u_{j}=u_{j}u_{i}=0 \rangle $
S
k
=
F
q
[
u
1
,
u
2
,
…
,
u
k
]
/
〈
u
i
3
=
u
i
,
u
i
u
j
=
u
j
u
i
=
0
〉
, where $1\leq i,j\leq k$
1
≤
i
,
j
≤
k
, $q=p^{m}$
q
=
p
m
, p is an odd prime. First, we define two new Gray maps $\phi _{k}$
ϕ
k
and $\varphi _{k}$
φ
k
, and study their Gray images. Further, we determine the structure of constacyclic codes and their dual codes, and give a necessary and sufficient conditions of constacyclic codes to contain their duals. Finally, we obtain some new quantum codes over $\mathbb{F}_{q}$
F
q
by using CSS construction, and compare the constructed codes better than the existing literature.