This can only be done out-of-the-box by setting the question direction to column-oriented. But I understand this is not always an option. To achieve this with row-oriented grid questions, what you'll need to do is create two grid question on the same page: the first with the four checkbox-type columns, the second with the open-end-type column. Then you can add this script to the page to combine the questions so they look like only one question:

[js]
<script>
$(document).ready(function(){
// Params
var questions = [];

// Run
if (!questions.length) {
$('.grid.question').each(function(){
questions.push(this.id.replace(/_div$/, ''));
});
}

var firstQ = questions.shift();

questions.forEach(function(question){
$('#' + question + '_div').hide();
});

if (!$('#' + firstQ + '_div .mobile_grid').length) {
var firstTbody = $('#' + firstQ + '_div .inner_table > tbody');
for (var row = 1; row <= $(firstTbody).children().length; row++) {
questions.forEach(function(question){
$(firstTbody).find('> :nth-child(' + row + ')').append($('#' + question + '_div .inner_table > tbody > tr:nth-child(' + row + ') > td:not(.corner_label_cell):not(.row_label_cell)'));
});
}
}

else {
var firstMobileGrid = $('#' + firstQ + '_div .mobile_grid');
for (var row = 1; row <= $(firstMobileGrid).children().length; row++) {
questions.forEach(function(question){
$(firstMobileGrid).find('> :nth-child(' + row + ') .mobile_grid_options').append($('#' + question + '_div .mobile_grid > :nth-child(' + row + ') .mobile_grid_options').children());
});
}
}
})
</script>
[/js]

The column widths may look a little off. If so, you could manually define the column widths with CSS. Here's an example that changes the first three columns:

[css]
<style>
#[% QuestionName() %]_div .inner_table > tbody > tr > td:nth-child(1) {
width: 10%;
}

#[% QuestionName() %]_div .inner_table > tbody > tr > td:nth-child(2) {
width: 10%;
}

#[% QuestionName() %]_div .inner_table > tbody > tr > td:nth-child(3) {
width: 10%;
}
</style>
[/css]

Add text boxes to grid