B737-800 CREW HAD A RWY INCURSION AT RWY 4L AT MDW.

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AFTER LNDG AT MDW; WE WERE DIRECTED TO THE RWY 22L HOLD PAD TO WAIT FOR OUR GATE TO OPEN. I POSITIONED THE ACFT ON TXWY R FACING E. AFTER APPROX 10 MINS OUR GATE CLRED AND WE WERE GIVEN DIRECTIONS TO TAXI. THE CTLR TOLD US TO TURN L ON TXWY N AND HOLD SHORT OF 4R. I FIGURED (ASSUMED) THAT HE MUST HAVE MEANT 'TURN L ON TXWY P; HOLD SHORT OF RWY 4R.' AS I BEGAN MAKING MY L TURN FROM TXWY N TO TXWY P; I REALIZED I HAD MADE A MISTAKE. A BEECH KING AIR HAD LIFTED OFF RWY 4L AND WAS APPROX 100 FT IN THE AIR. OUR HORIZ DISTANCE TO ACFT WAS APPROX 1000 FT. AS WE CROSSED THE HOLD SHORT LINE; I HEARD GND TELL US TO STOP. HE THEN CLRED US TO HOLD SHORT OF RWY 4R AT TXWY P. WE ARE ALMOST ALWAYS GIVEN TXWY P AS THE TXWY TO CROSS RWY 4R AND I THINK THAT WHEN WE RECEIVED OUR INITIAL CLRNC; I DID WHAT I HAVE DONE HUNDREDS OF TIMES BEFORE. THERE WERE A NUMBER OF ACFT PUSHED BACK; BLOCKING THE RAMP/TXWYS BY TXWY N AND I MISTAKENLY ASSUMED THAT THE CTLR WANTED US ON TXWY P; ESPECIALLY SINCE TXWY P PROVIDED A STRAIGHT IN APCH TO OUR GATE.