DNA is housed within the nucleus, but the mRNA code needs to leave in order to be translated into a protein. How does the mRNA code leave the nucleus if the nucleus is surrounded by the nuclear envelope?

Through nuclear pores.

Explanation:

The nucleus of a eukaryotic cell is double membrane-enclosed organelles which enclose the genetic material of the cell.

Although the nucleus contains the nuclear membrane but the molecules are exported and imported into the cells through small pores known as the nuclear pores.

The mRNA is synthesised through the process of the transcription is exported out of the nucleus through these nuclear pores.

Thus, the nuclear pore is correct.