You basically need enemies that are of significant level to drop Mark XI gear. I think your best hopes are thus Ker'rat and Vice Admiral Fleet Actions.
Basically, the FAs and Ker'rat/Otha opposition is always scaled to a tier of play, so it sits somewhere between the lowest and the highest level in that tier. Since we are only Vice Admiral 1 currently this means they are higher level then we are.
Exploration and Featured Episodes scale to your specific level, so the enemies are of lower level and have no or only a very very low chance to drop Mark XII gear.