Wilmer S. Cody, a nationally known educator and superintendent of the Birmingham, Ala., schools, is the likely selection to lead Montgomery County's school system when Superintendent Edward Andrews retires in July, county school officials said yesterday.

Cody, 46, has been an educator for 23 years and is well known in education circles for his work in implementing integration programs. In Birmingham, where schools have been under federal court order to desegregate since 1965, Cody is credited by school and municipal officials with a successful effort over the last decade to foster desegregation and raise test scores.

In 1967 he implemented a voluntary integration program in the Chapel Hill, N. C., school system, which he headed before moving to Birmingham.

Cody, who was one of three finalists in 1979 for the Fairfax County superintendent's job, was praised yesterday by a national education official as well as officials in the Alabama city.

"He is probably one of the best superintendents in the country," said Paul Salmon, executive director of the American Association of School Administrators, when queried by a reporter. "He has overseen a big change in demography in Birmingham, but he has done it marvelously. . . . He is like E.F. Hutton: When he speaks, people listen."

Montgomery County officials said Cody has not yet been formally offered the job, but probably will be if no problems arise next week when he arrives to meet with school officials and community leaders.

He emerged as the top candidate after a review of more than 100 applicants.

"He is a man who has ideas and who makes them happen," said board President Blair Ewing, who said there was an uncommonly high level of agreement among board members about Cody's selection. Five of the seven board members went to Birmingham last weekend to meet with Cody and interview various civic and school officials.

In addition to implementing a number of specialized academic programs in Birmingham designed to attract white students, Cody yesterday also was credited with raising test scores from below the national average to equal or above it, getting voters to approve the first property tax increase in 50 years and securing funding to begin additional math and reading tutoring programs.

If Cody is offered and accepts the Montgomery County job, he will face a school system dramatically different from the one he now heads. Birmingham is an urban school system with 45,000 students, 80 percent of whom are black, and a current budget of $71 million. The Montgomery school system is a predominantly suburban one with 92,500 students and a budget this year of $353 million. A quarter of the students in Montgomery County are minority.

Both Cody and Montgomery school officials said yesterday they believe his experience with a city school system would be an asset to the county as it looks for ways to deal with an increasingly urbanized school system.

Cody said that what interests him about the Montgomery school district is "its higher expectations in intellectual skill. This is becoming of great importance in the country, and the nature of Montgomery County obviously allows this."

Even those described as sometime detractors of Cody were generous in their praise yesterday. "He's done it all," said Birmingham School Board President Louis Dale. "We've had our professional disagreements, but they've always been minor. . . . During the last decade Dr. Cody, with the help of federal and state grants, has initiated almost all the new programs we have here."