The noun (Substantiv/Nomen) Baukosten is feminine in German. Therefore, the correct definite article in the nominative singular is die. So, you say: die Baukosten.
construction costs
This word is composed and its gender is always determined by the root word.
Die Gesamtkosten für die Errichtung eines Bauwerks.
The total costs for the construction of a building.
Die Baukosten sind unerwartet gestiegen.
The construction costs have unexpectedly increased.