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It is shown that the residue code of a self-dual Z 4 -code of length 24k (resp. 24k + 8) and minimum Lee weight 8k + 4 or 8k + 2 (resp. 8k + 8 or 8k + 6) is a binary extremal doubly even self-dual code for every positive integer k. A number of new self-dual Z 4 -codes of length 24 and minimum Lee weight 10 are constructed using the above characterization.doi:10.3934/amc.2016035 fatcat:l32fodtntfbynp4xxpw7oh7hse