Let
K
=
Q
(
−
ℓ
)
K=Q(\sqrt {-\ell })
be an imaginary quadratic field with ring of integers
O
K
\mathcal {O}_K
, where
ℓ
\ell
is a square free integer such that
ℓ
≡
3
mod
4
\ell \equiv 3 \mod 4
, and let
C
=
[
n
,
k
]
C=[n, k]
is a linear code defined over
O
K
/
2
O
K
\mathcal {O}_K/2\mathcal {O}_K
. The level
ℓ
\ell
theta function
Θ
Λ
ℓ
(
C
)
\Theta _{\Lambda _{\ell } (C) }
of
C
C
is defined on the lattice
Λ
ℓ
(
C
)
:=
{
x
∈
O
K
n
:
ρ
ℓ
(
x
)
∈
C
}
\Lambda _{\ell } (C):= \{ x \in \mathcal {O}_K^n : \rho _\ell (x) \in C\}
, where
ρ
ℓ
:
O
K
→
O
K
/
2
O
K
\rho _{\ell }:\mathcal {O}_K \rightarrow \mathcal {O}_K/2\mathcal {O}_K
is the natural projection. In this paper, we prove that: i) for any
ℓ
,
ℓ
′
\ell , \ell ^\prime
such that
ℓ
≤
ℓ
′
\ell \leq \ell ^\prime
,
Θ
Λ
ℓ
(
q
)
\Theta _{\Lambda _\ell }(q)
and
Θ
Λ
ℓ
′
(
q
)
\Theta _{\Lambda _{\ell ^\prime }}(q)
have the same coefficients up to
q
ℓ
+
1
4
q^{\frac {\ell +1}{4}}
, ii) for
ℓ
≥
2
(
n
+
1
)
(
n
+
2
)
n
−
1
\ell \geq \frac {2(n+1)(n+2)}{n} -1
,
Θ
Λ
ℓ
(
C
)
\Theta _{\Lambda _{\ell }} (C)
determines the code
C
C
uniquely, iii) for
ℓ
>
2
(
n
+
1
)
(
n
+
2
)
n
−
1
\ell > \frac {2(n+1)(n+2)}{n} -1
, there is a positive dimensional family of symmetrized weight enumerator polynomials corresponding to
Θ
Λ
ℓ
(
C
)
\Theta _{\Lambda _\ell }(C)
.