How do I get my doberman pup to stop ripping up our lawn?

Our five month old doberman puppy LOVES to rip up large chunks of gr whenever she goes outside to play. We have lots of toys for her to play with out there, but when she gets bored with one, instead of getting up for a different toy, she lies there and starts ripping up the gr. I've tried fussing when I see her do it (not harshly but enough to get my point across to her), and then I try to give her a different toy to play with. But she just runs from me with the gr in her mouth, and then by the time I get her to come to me (with a whistle blow and a treat), the meaning seems to be lost. I've also tried the "drop it" command, but it's like she knows I can't enforce it when she can just run from me. She does well with this command when we work on it inside with other things. I've also tried treats for dropping it... but then she starts ripping up the gr just to get a treat! She also digs in the garden whenever I go inside for a minute. It's almost like she's punishing ME for going inside instead of staying out there with her. What do I do??