Auto-Train Corp. announced yesterday it has signed an agreement to manufacture 10,000 covered railroad hopper cars over the next 10 years for PLM Inc., a San Francisco rail car leasing company.

Auto-Train President Eugene Kerik Garfield said his company will receive at least $60 million under the contract, and PLM officials said the total value of the order could exceed $400 million.

The order is the first to be placed with Auto-Train's newly organized subsidiary, Railway Services Corp., which has yet to build its first freight car.

The agreement calls for Auto-Train to assemble the first 1,000 cars from "kits" of parts supplied by PLM. After that Auto-Train may manufacture the car bodies for the remaining 9,000 cars, the company said.

Under the contract, PLM is to pay Auto-Train $6,000 for assembling each car for PLM, and about $40,000 for each car it builds from scratch.

Auto-Train's announcement said the cars are to be built in a Seaboard Coast Line Railroad plant in Portsmouth, Va. that Auto-Train has leased with an option to purchase.

Under the contract, however, Auto-Train must by Nov. 30 "use its best efforts" to invest $750,000 in the Portsmouth plant to prepare it for operation.

The announcement said Auto-Train expects to raise that money through a new public stock offering some time in the next three months. Auto-Train executives have discussed several possible methods of raising money for the financially troubled railroad recently, the latest of them a plan to sell new common stock.

The Interstate Commerce Commission, however, has indicated it will not approve issuance of any new securities by Auto-Train until the company repays more than $800,000 in refunds due to passengers.

Last week, the Seaboard agreed to give Auto-Train until the first of the year to pay overdue charges due Seaboard for use of tracks and train crews to carry the Auto-Train from Lorton, Va. to Florida.

That extension also requires Auto-Train to come up with large amounts of cash before the end of the year.

The hopper contract was announced late yesterday, after increased trading in Auto-Train's shares had pushed the price of the stock from 3 1/8 to 4 on the American Stock Exchange. The stock closed at 3 3/4 per share, up 5/8 and was the Amex's biggest percentage gainer, as the value of each share increased by 20 percent.

The stock has bounced back and forth between $2 and $7 a share in the past few months, propelled by positive and negative reports about the company's financial problems. Because its railroad business has never produced consistent profits, Auto-Train several months ago said it was diversifying into rail car maintenance, repair and construction.

PLM Inc., for which Auto-Train is to become the exclusive hopper car supplier, was organized in 1972 to arrange the sale and lease of freight cars, most often as a tax-sheltered investment for high-income persons. The company has leased 1,700 freight cars since it was organized.