Type II code over F2 + uF2 + u2F2

Motivated by the work of Dougherty, Ling and Betsumiya, we define type II codes over R = F₂ + uF₂ + u²F ₂ as self-dual codes with Lee weights a multiple of 4. A new Gray map between codes over R and codes over F₂ is defined. The existence of self-dual code over R is examined. Properties of the Gray map which take self-dual codes over R to self-dual codes over F₂ are studied