Solved with:
<?php
add_filter( 'body_class', 'alter_body_class', 20, 2 );
function alter_body_class( $classes ) {
foreach( $classes as $key => $value ) {
if ( $value === 'page' ) {
unset( $classes[ $key ] );
}
}
return array_merge( $classes, array( 'home' ) );
}
?>