George Tower
It's very close indeed. Depends on the pax configuration, actual empty operating weight (I wonder what extra weight equipment is installed), how much cargo/freight is onboard in addition to baggage, what engines (V2500 or CFM). For 134 pax, 1000kg extra cargo, 39225kg OEW and V2500, the aircraft can haul a full load out of a level 6000' feet runway (but not 5900') for your 4000' and 25 degC.
That is too close to call. And if any airport has a 6000 foot runway for jet ops (which is generally held to be too short), it's odds on that there are obstacles at each end which mean that the climb performance could very likely govern and reduce the load. However now that this first pass suggests that it will fit, it's justified to get a performance engineer, aircraft actual data plus the airport Type A charts and runway data for a more detailed analysis.