maybe someone can help me out?
I haven't tried the 32bit version for a while now but I do have the same card running fine with the 64bit Beta version on my X1Carbon.
BTW, you didn't state which Elive version you are using.
If it's Stable version (and the xserver version/date suggests that), expect more issues as it's quite old and doesn't support all modern hardware.
looking at the logs, where we can see the kernel version, is the beta version, but hes using the kernel 4.9 which is pretty old
Please try an updated beta version and with the 5.x kernel (next version 3.8.19 will include 5.10), it will probably work with an updated kernel
near the top, it does not say "Release date: 2012-07-27" ?