Construction of Foxborough High School’s first artificial turf field has begun, a $1.6 million-plus project that will be ready for games in October. A majority of voters approved the project at a Town Meeting in December. A second phase, which calls for a track, bleachers, and other amenities — at an additional cost of about $1.8 million — could come up for a vote at another time. The current project, being performed by Green Acres Landscape & Construction Co. of Lakeville, is funded by donations, town money, and a grant from the National Football League. A pair of grass fields will be constructed in the back of the high school and should be ready for use in 2015.