  We use the three-dimensional Heisenberg model with site randomness as an
effective model of the compound Sr(Fe$_{1-x}$Mn$_x$)O$_2$. The model consists
of two types of ions that correspond to Fe and Mn ions. The nearest-neighbor
interactions in the ab-plane are antiferromagnetic. The nearest-neighbor
interactions along the c-axis between Fe ions are assumed to be
antiferromagnetic, whereas other interactions are assumed to be ferromagnetic.
From Monte Carlo simulations, we confirm the existence of the
double-$\boldsymbol{q}$ ordered phase characterized by two wave numbers,
$(\pi\pi\pi)$ and $(\pi\pi0)$. We also identify the spin ordering pattern in
the double-$\boldsymbol{q}$ ordered phase.
