Can't to reinstall OS X. Unable to write the last block of the device

Hi, I am having trouble with my 2013 MacBook Air a1465. Turning it on displays an image of a folder with a question mark inside. Looking for how to solve the problem, I tried to clean the NVRAM, with ALT + CMD + P + Q. NVMRAM was successfully cleaned but the issue was not resolved so I tried to reinstall the system through OS X Utilities. When turning on the computer I press the CMD + R keys, I correctly enter OS X Utilities. If I select Reinstall OS X option, a screen opens to install OS X Mountain Lion, but when selecting the disk no disk appears. Again in the menu of OS X Utilities, I enter the DIsk Utility option, here if the disk appears (120gb SSD), but when trying to format it or create a partition after a few minutes an error appears "Unable to write the last block of the device ”, and the disk disappears from the list. To see the disk again I have to clean the NVRAM again.

I tried erase with the formats Mac OS Extended (Journaled), Mac OS Extended (Journaled, Encrypted) and the message is always the same. I also tried to create a partition that occupies the entire disk with the same two formats, and I also get the same error .

I also tried to create a disk image so I could restore it later. I select New Image, try to save it to an external disk, and after a few minutes a message appears saying that the device is not configured.

I also want to comment that you start a Linux Live-CD, the computer starts correctly, but it never detects the disk, neither when installing the OS from the Kali Linux installation menu, nor after booting the Live-CD with the command fdisk -l.

I attach an image with information from the disc.

TOSHIBA THNSN2128GSPS

output diskutil list

Is there a way to do a complete formatting of the disk? Or should I buy a new album?

Actualización (17/07/20)

Hello, thanks for answering. I started the system with option + cmd + r, and the system booted with OS X Catalina. I tried to reinstall macOS, but the installer cannot find the disk. So I tried to format the disk using Disk Utility, but it fails to complete the process.

OS X Installer

SSD Info Disk Utility

Disk Utility First Aid

Disk Utility Erase

Hello, thanks for answering. Start the system with option + cmd + r, and the system booted with OS X Catalina. I tried to reinstall macOS, but the installer cannot find the disk. So I tried to format the disk using Disk Utility, but it fails to complete the process.

Output command diskutil eraseDisk HFS + disk22 / dev / disk23:

Started erase on disk23

Unmounting disk

Creating the partition map

[ \ 0%..10%..20%..30%..40%..50% . . . . . . . . . . . . . . . . . . . . . . ] 50.0%

Error: -69877 Couldn't open device

Output command diskutil list