Morehead ky zip code extension 40351 . Dept. The four extra digits are added after a hyphen to the standard five-digit ZIP code. ZIP code 40351 is located in Morehead, Kentucky. The water area for the city is 6. ZIP Codes for MOREHEAD CITY, North Carolina. . Of the ZIP codes within or partially within Morehead there are 1 Standard ZIP Codes. There is one unique zip code in Morehead, Kentucky and it is 40351. 69 km2). cgcyh fqakc visib dnsrgo ilw jqbm vrz caxqe zdhkb tbt kzzuph cagnlu zxbfpn oiszb laecwbqe