  The Hirota equation is one of the integrable higher-order extensions of the
nonlinear Schr\"odinger equation, and can describe the ultra-short optical
pulse propagation in the form $iq_t+\alpha(q_{xx}+ 2|q|^2q)+i\beta (q_{xxx}+
6|q|^2q_x)=0,\, (x,t)\in\mathbb{R}^2\, (\alpha,\,\beta\in\mathbb{R})$. In this
paper, we analytically explore the asymptotic behaviors of a soliton gas for
the Hirota equation including the complex modified KdV equation, in which the
soliton gas is regarded as the limit $N\to \infty$ of $N$-soliton solutions,
and characterized using the Riemann-Hilbert problem with discrete spectra
restricted in the intervals $(ia, ib)\cup (-ib, -ia)\, (0<a<b)$. We find that
this soliton gas tends slowly to the Jaocbian elliptic wave solution with an
error $\mathcal{O}(|x|^{-1})$ (zero exponentially quickly ) as $x\to -\infty$
($x\to +\infty$). We also present the long-time asymptotics of the soliton gas
under the different velocity conditions: $x/t>4\beta b^2,\, \xi_c<x/t<4\beta
b^2,\, x/t<\xi_c$. Moreover, we analyze the property of the soliton gas for the
case of the discrete spectra filling uniformly a quadrature domain.
