When the card is minimised it is impossible to say: is it just empty or does it have some content and is just minimised.
Example: can you say which of these cards are empty and which are minimised?
I suggest to add some visual sign for minimised cards with some text in their body, that the card is not empty:
_ or just
+ for example (near of the Title, I suppose).
Clicking on this sign may restore the card (like pressing right arrow).