Just add
xAxis: {
...
lineWidth: 0,
minorGridLineWidth: 0,
lineColor: 'transparent',
...
labels: {
enabled: false
},
minorTickLength: 0,
tickLength: 0
}
to the xAxis definition.
Since Version 4.1.9 you can simply use the axis attribute visible:
xAxis: {
visible: false,
}