Does saying, "Insha'Allah, I haven't contacted him," when intending to send a text message and not make a phone call, count as a false oath?

The statement: "In sha Allah, I did not contact him" is not a legal oath, because an oath is made by swearing by one of the names of Allah Almighty using one of the letters of oath (waw, ta', or ba'). If you intended by this phrase to deny the usual phone call, then there is no blame on you, and it is not considered a lie; rather, it falls under the category of elliptical remarks (ma'arid).