Let (G, +) be a finite abelian group and (C, +)<; (Gⁿ, +) be an additive code with dual (C^⊥,.) <; (Gⁿ, + .). Consider a lattice (L, ∩, +) of subgroups of (Gⁿ, +) and its dual lattice (L^⊥, ., ∩) of subgroups of the character variety (Gⁿ, .). We say that L and L^⊥ are saturated if their unique elements of maximal order are Gⁿ ∈ L, respectively, G^⊥ ∈ L^⊥. The present note generalizes Randriambololona's Riemann-Roch Theorem for sections of F_q-linear codes C ⊂ Fⁿ_q with values in subspaces of Fⁿ_q to L-valued sections of C and L^⊥-valued sections of C^⊥. That provides natural Mac Williams identities for C, C^⊥ with respect to saturated L, L^⊥. If C ⊂ Fⁿ_q is an F_q-linear code and (H, ∩, +) is the Hamming lattice of the coordinate subspaces of Fⁿ_q, our Mac Williams identities reduce to the classical ones.