Hi and welcom to the forum
Firstly are these highs every morning?
Are you sure that it's not night time hypo's?
I would to a couple of night-times readings, around 2-3am as this is the time our hormone activity is at it's lowest ebb and our BG's are generally at there lowest point..
It is also worth extended this testing through out the night, you don't have to wake up every hour on one night, but can spread it over different nights, so one night you test at 10 and 11pm, next night or in a couple of nights test at 12pm and 1am, etc or you can do it in larger blocks this will give you a picture of whats happening to your BG's over-night and as you approach wake up, if DP then you should start to see you BG climb from anywhere around 4am onwards to mid morning...
Other reasons, could be that your levimer isn't lasting a full 24 hours, so take a look at what time you are injecting your levimer, if it seems that it isn't lasting 24 hours, you have two options, either move the injection time around to time the tail off better or split the levimer into 2 injections to give a more even spread... Spliting the levirmer injection can help with the effects of DP as it you can increase the dose to cover DP without overloading yourself later..
Other things to consider, is has your routine, exercise or activity changed in the day, or are you eating different types of foods more so teatime onwards.. As these can effect our BG's for a lot longer than one might think..
Finally do you carb count, and have you've done a DAFNE type course?
P.S
I like the mastiff he/she looks lovely, I have two dogs of my own, a German Shepherd and a German Shepherd cross Corgi, all German Shepherd (long haired) with little Corgi legs with dropped ears