I've been reading about self dual codes, and the literature says that there is a quaternary self dual code $$i_2 \otimes \mathbb{F}_4$$where $i_2 = {\{00,11}\}$ is a binary self dual code and $\mathbb{F}_4$ is the field of four elements.
This code has weight enumerator $x^2 + 3y^2$, and so only has $4$ codewords.
What is this code? What does $i_2 \otimes \mathbb{F}_4$ mean?
Hint: View $i_2$ as ${\Bbb F}_2$-space of dimension $1$, basis $\{11\}$, and ${\Bbb F}_4$ as ${\Bbb F}_2$-vector space of dimension $2$, basis $\{1,\alpha\}$, where $\alpha$ is a zero of the irreducible polynomial $x^2+x+1$. In this way, the tensor product $i_2\otimes_{{\Bbb F}_2} {\Bbb F}_4$ is well-defined and has dimension $2$ (as the product of dimensions).