I modified the answer from ruakh and this seem to work perfectly with mysql.
SELECT
table_a.code,
table_a.emp_no,
table_b.city,
table_b.county
FROM table_a a
LEFT JOIN table_b b
ON b.code = a.code
AND b.id = ( SELECT id FROM table_b
WHERE table_b.code = table_a.code
LIMIT 1
)
;