Hi, it seems like the bug with either Atom or XRDP discussed in Atom issue here: atom/atom#4360 is keeping VSCode from working in Ubuntu when you connect to it with RDP.
Trying to launch the app gives the following output:

Xlib: extension "XInputExtension" missing on display ":10.0".
Xlib: extension "XInputExtension" missing on display ":10.0".
libGL: OpenDriver: trying /usr/lib/x86_64-linux-gnu/dri/tls/swrast_dri.so
libGL: OpenDriver: trying /usr/lib/x86_64-linux-gnu/dri/swrast_dri.so
libGL: Can't open configuration file /home/hannesne/.drirc: No such file or directory.
libGL: Can't open configuration file /home/hannesne/.drirc: No such file or directory.
libGL error: No matching fbConfigs or visuals found
libGL error: failed to load driver: swrast
bash: cannot set terminal process group (-1): Inappropriate ioctl for device
bash: no job control in this shell
Xlib: extension "XInputExtension" missing on display ":10.0".
Xlib: extension "XInputExtension" missing on display ":10.0".
[ , [Error: channel closed] ]

This happens regardless of using the MATE or LFCE desktop.
An output of GLXInfo gives the following:

libGL error: No matching fbConfigs or visuals found
libGL error: failed to load driver: swrast
name of display: :10.0
display: :10 screen: 0
direct rendering: No (If you want to find out why, try setting LIBGL_DEBUG=verbose)
server glx vendor string: SGI
server glx version string: 1.2
server glx extensions:
GLX_EXT_import_context, GLX_EXT_visual_info, GLX_EXT_visual_rating
client glx vendor string: Mesa Project and SGI
client glx version string: 1.4
client glx extensions:
GLX_ARB_create_context, GLX_ARB_create_context_profile,
GLX_ARB_create_context_robustness, GLX_ARB_fbconfig_float,
GLX_ARB_framebuffer_sRGB, GLX_ARB_get_proc_address, GLX_ARB_multisample,
GLX_EXT_buffer_age, GLX_EXT_create_context_es2_profile,
GLX_EXT_fbconfig_packed_float, GLX_EXT_framebuffer_sRGB,
GLX_EXT_import_context, GLX_EXT_texture_from_pixmap, GLX_EXT_visual_info,
GLX_EXT_visual_rating, GLX_INTEL_swap_event, GLX_MESA_copy_sub_buffer,
GLX_MESA_multithread_makecurrent, GLX_MESA_query_renderer,
GLX_MESA_swap_control, GLX_OML_swap_method, GLX_OML_sync_control,
GLX_SGIS_multisample, GLX_SGIX_fbconfig, GLX_SGIX_pbuffer,
GLX_SGIX_visual_select_group, GLX_SGI_make_current_read,
GLX_SGI_swap_control, GLX_SGI_video_sync
GLX version: 1.2
GLX extensions:
GLX_ARB_get_proc_address, GLX_EXT_import_context, GLX_EXT_visual_info,
GLX_EXT_visual_rating, GLX_MESA_multithread_makecurrent
OpenGL vendor string: Mesa project: www.mesa3d.org
OpenGL renderer string: Mesa GLX Indirect
OpenGL version string: 1.3 Mesa 4.0.4
OpenGL extensions:
GL_ARB_imaging, GL_ARB_multitexture, GL_ARB_texture_border_clamp,
GL_ARB_texture_cube_map, GL_ARB_texture_env_add,
GL_ARB_texture_env_combine, GL_ARB_texture_env_dot3,
GL_ARB_transpose_matrix, GL_EXT_abgr, GL_EXT_blend_color,
GL_EXT_blend_minmax, GL_EXT_blend_subtract, GL_EXT_draw_range_elements,
GL_EXT_multi_draw_arrays, GL_EXT_texture_env_add,
GL_EXT_texture_env_combine, GL_EXT_texture_env_dot3,
GL_EXT_texture_lod_bias, GL_SGIS_texture_border_clamp,
GL_SUN_multi_draw_arrays

8 GLX Visuals
visual x bf lv rg d st colorbuffer sr ax dp st accumbuffer ms cav

id dep cl sp sz l ci b ro r g b a F gb bf th cl r g b a ns b eat

0x024 24 tc 1 24 0 r y . 8 8 8 0 . . 0 16 0 0 0 0 0 0 0 None
0x025 24 tc 1 24 0 r y . 8 8 8 0 . . 0 16 8 16 16 16 0 0 0 None
0x026 24 tc 1 24 0 r y . 8 8 8 8 . . 0 16 8 16 16 16 16 0 0 None
0x027 24 tc 1 24 0 r . . 8 8 8 8 . . 0 16 8 16 16 16 16 0 0 None
0x028 24 dc 1 24 0 r y . 8 8 8 0 . . 0 16 0 0 0 0 0 0 0 None
0x029 24 dc 1 24 0 r y . 8 8 8 0 . . 0 16 8 16 16 16 0 0 0 None
0x02a 24 dc 1 24 0 r y . 8 8 8 8 . . 0 16 8 16 16 16 16 0 0 None
0x02b 24 dc 1 24 0 r . . 8 8 8 8 . . 0 16 8 16 16 16 16 0 0 None

Any suggestions?