A NON CRITICAL ACFT PROB CAUSES A DISTR AFTER TKOF RESULTING IN AN ALT OVERSHOOT.

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ON CLBOUT AFTER TKOF FROM FTW; WE WERE INSTRUCTED TO CLB AND MAINTAIN 4000 FT. ON CLB IN IMC; THE CAPT NOTICED ONE ANTISKID LIGHT HAD ILLUMINATED; INDICATING A FAILURE ON 1 WHEEL OF THE ANTISKID SYS. THE CAPT CALLED FOR CHKLIST PROCS. I COMPLETED THE AFTER TKOF CHKLIST AND BEGAN LOOKING FOR THE APPROPRIATE CHKLIST FOR AN ANTISKID FAILURE. WHILE I WAS LOOKING; THE ALT ALERTER INDICATED 1000 FT BEFORE LEVELOFF. I CALLED '1000 FT TO GO;' WHICH THE CAPT ACKNOWLEDGED. I DID NOT SEE ANY PROCS ON THE EMER CHKLIST; AND ASKED THE CAPT IF IT WAS LISTED UNDER ABNORMAL PROCS. THE CAPT POINTED TO A CHART ON THE BACK COVER WHICH INDICATED THE CORRECT PAGE. AS I WAS READING THROUGH THE PROCS; THE CAPT MADE A REMARK ABOUT OUR ALT. I LOOKED UP AND SAW THAT WE WERE AT 4700 FT. ATC QUESTIONED US ABOUT OUR ALT JUST AS THE CAPT BEGAN TO MAKE A CORRECTION; AND THEN CLRED US TO 6000 FT. THE CAPT RESUMED THE CLB AND THE FLT PROCEEDED UNEVENTFULLY. THE DISTR FROM THE ANTISKID LIGHT WAS THE PRIMARY CAUSE FOR BUSTING THE ALT. IT SHOULD NOT HAVE BEEN; SINCE A FAILURE WOULD HAVE ONLY IMPACTED OUR NEXT LNDG. HOWEVER; WE WERE THINKING AHEAD TO THE NEXT LNDG INSTEAD OF MINDING OUR ALT.