Dic: stretch as a noun meaning ‘extension to or beyond the ordinary limit’

■ stretch: (5) extension to or beyond the ordinary limit:

• running at full stretch
• by no stretch of the imagination
• beyond any stretch of his understanding

...WordNet

• Her husband was not a womaniser by any stretch of the imagination...
• My family wasn't wealthy by any stretch of the imagination.
• It is not a great movie by any stretch of the imagination.

■ If you say that something is not true or possible by any stretch of the imagination, you are emphasizing that it is completely untrue or absolutely impossible.

■ by any stretch (of the imagination): spoken. used to emphasize that a negative statement is true.

■ not by any stretch of the imagination(by no stretch of the imagination): used for saying that you think something cannot be true or possible no matter how hard you try to imagine it.

... cobuild, ldoce, macmillan