Why SLOC is bad as an individual metric of productivity
Think of code as a block of clay/stone. You need to carve, say 10 statues. It's not how many statues you carve that counts. It's how well you've carved it that counts. Similarly it's not how many lines you've written but how well they are functioning. In case of code LOC can backfire as a metric this way.
Productivity also changes when writing a complex piece of code. It takes a second to write a print statement but a lot of time to write a complex piece of logic. Not all fingers are equal.
How SLOC can be used to your benefit
I think SLOC for defect % is a good metric. Yes the difficulty level comes into play but this is a good parameter that the managers can throw around while doing business. Try to think from their perspective too. They don't hate you or your work, but they need to tell customers that you're the best and for that they need something tangible. Give them what you can :)