If you are extremely lucky and have kept the cane outside it might still be alive and you can propagate the rose as cuttings. there are many helpful threads in this forum that shows you how to do this. But It would be best if you start with a new cane from the rose if you want to do this.

Here is a link that might be useful: propagate rose cuttings

We just had the same discussion on the Rose Hybridizer Association's forum. The buds on those stems were just starting to swell, not nearly as far along as yours. It was decided that even those stems were too far along to successfully root.
The stems must be dormant when attempting to root or graft.
Sorry, but I don't it will root successfully, but you can try, you're not going to lose anything by trying.

I disagree that the cutting has to be dormant to be rooted successfully. I have rooted many cuttings that were actively growing when the cutting was taken. The important thing is to remove all or almost all of the leaves.(I usually leave one if the leaves are mature and remove all of them if they are still developing.) You do not want the cutting wasting energy growing leaves. It is also important to get it started as soon as possible after you have taken the cutting.