In this sentence (I would assume), 저만큼 and 그만큼 are probably interchangeable since we don't really know the context of the sentence. We don't know the context as in, we don't know if the speaker is using another object to show the size of his bag (think of comparing? Like "My bag is as big as that" with "that" being a car you are pointing at.) If the speaker is comparing then I believe you'd used 저만큼. If not, and you are perhaps...pretending to measure with your hands or referencing a measurement unit (Someone says their hand is 10 cm wide, then you would use ...그만큼... instead of 저만큼, since you aren't comparing two objects.), then you would use 그만큼.
Aside from that somewhat ambiguous difference, 저만큼 can also be used to say "to that extent", where 그만큼 is generally not used in that case. There is an example in this lesson that says that "I speak Korean to that extent" or something (in this case, indicating your limit for a certain skill aka. speaking Korean).
Gonna need a mod to expand and verify this information.