Flight Crew Air Transport Pilot (ATP); Flight Crew Instrument; Flight Crew Multiengine
Flight Crew Last 90 Days 329; Flight Crew Type 12000
Situational Awareness; Communication Breakdown
Deviation - Altitude Overshoot; Deviation / Discrepancy - Procedural Clearance; Deviation / Discrepancy - Procedural Published Material / Policy
Flight Crew Became Reoriented
Human Factors
Passing approximately 16;000 feet; ZZZ Center asked if we were climbing. We answered 'Yes; climbing via the ZZZZZ 4 SID; with top altitude FL230.' ZZZ Center asked if we were given 14;000 feet as our top altitude. We answered 'No.' Flight continued normally. After further conversation between pilots; the Pilot Monitoring realized that the initial clearance was to climb via except maintain 14;000 feet. Pilot Monitoring incorrectly set 23;000 feet on the MCP after VNAV was selected during climb. 23;000 feet is the top altitude as published on the ZZZZZ 4 SID. PF did not correct the error. On subsequent check in with ZZZ Approach and ZZZ Center; the Pilot Monitoring said we were 'climbing via'; not 'climbing via to 14;000 feet.' ATC did not correct or question; until separate transmission from ZZZ Center passing 16;000 feet as stated.
B737-700 Captain reported a miscommunication resulted in them overshooting a cleared altitude departing.