I don't think it is a Kenmore. Could be made by the same maker as made Kenmores thought.
If it's a Kenmore it would have a serial number like this: 158-15000 or similar on it somewhere. Usually under the bed on the lip.
More likely it's a Asian made machine that was made for many many different companies.
You could try Relics {
http://www.tias.com/stores/relics/ }, they have photos of the machines to look at.
Joe