Well historically Type II codes are the so called doubly even self dual binary codes.(There are five types the Vth being trivial. Search for Gleason Pierce Turyn theorem on divisible codes). Then Conway and Sloane define Type II lattices by analogy. So I introduced Type II Z4 codes because construction A yields Type II lattices (see my paper with Bonnecaze Mourrain and Bachoc), In that setting the Euclidean metric is natural. Now over other rings we want to produce binary Type II codes hence the metric used for F2+uF2 or even F4.