IgorC while there might be some sliver of hope, NO, that is too old. I do not think it would be a quality investment of your time. There is no official age range stated because that they are concerned about that being discriminatory but consider that the average work experience at GSB is 4 years. The average age is 27. It would be awkward to have a 38 year old man in class with 25 year olds, would throw off the dynamic and unfortunately on campus recruiters are looking for people within a specific age range.
You would be better suited to apply to the
Stanford MSx program. I believe it requires 8 years of work experience. It's specifically intended or mid-career professionals who want to do a full time one year program. To increase your odds, might also apply to sister programs similar to Stanford MSx called Sloan Fellows at MIT, and then one also at LBS.
Your main option is to go for executive MBA programs. You're also too old for most part-time MBA programs or one year programs but its not entirely impossible; would require doing some research.
IgorC
Do I have any chance to join the Stanford MBA program being 37 years old?