CIEMAT-QI4 is a quasi-isodynamic stellarator configuration that simultaneously features very good fast-ion confinement in a broad range of β values, low neoclassical transport and bootstrap current, and ideal magnetohydrodynamic stability up to . In this paper it is shown that CIEMAT-QI4 also exhibits reduced turbulent transport. This is demonstrated through nonlinear electrostatic simulations with the gyrokinetic code stella, including kinetic ions and electrons. The relation between reduced turbulent transport and the fact that CIEMAT-QI4 very approximately satisfies the so-called maximum-J property is discussed.