# Which hash function can be used to get $w=H(d)\in F^n$ case?

I am trying to implement a cryptographic scheme. For a arbitrary message $d$ , I need a Hash Function $\mathbb{H}$ that can compute the hash value $w=\mathbb{H}(d)\in \mathbb{F}^n$. Here $F$ is a finite field of order four.

I can not find any hash function which outputs field values.

You need to make your question more precise. There is always the trivial hash function that maps very w to the zero vector of F^n. What properties should your hash function satisfy ?