How to fix a contour color of a 2D cut with gnuplot

Please I would like to have unique black lines for my 2D contour.

set terminal png size 800,800 font 'Times New Roman, 12'
set output 'TH1.png'
set view map
set pm3d map
unset surface
set cont base
set cntrparam levels 50
set isosamples 10
unset key 
set xrange[0:180]
set yrange[0:180]
set xlabel '{/Symbol q}'
set ylabel '{/Symbol q}''
set palette rgb 33,13,10
splot 'TH1TH2.dat' w ima, 'TH1TH2.dat' w l lt -4 lw 1.6

For values great than 2000 I want a red contour. Can someone help me? Here is my 2D cut But I would like to have only the black lines. link for the data

It would be ideal if we could use the original data (maybe minimized). Anyway, the following example creates its own data. If you need further explanations please let me know.

Script:

### contour lines with custom colors
reset session

set pm3d
set contour 
set cntrparam levels 20

### create some test data
set table $Data
    set isosamples 100
    set samples 100
    f(x,y)=(sin(1.3*x)*cos(.9*y)+cos(.8*x)*sin(1.9*y)+cos(y*.2*x))*4000/3.+2000
    splot [-5:5][-5:5] f(x,y)
unset table

set palette rgb 33,13,10
set size ratio 1
unset key
set tics out
set view map
set xrange[:] noextend
set yrange[:] noextend

myColor(v) = v>=2000 ? 0xff0000 : 0x000000

plot $Data index 0 u 1:2:3 w image, \
        '' index 1:999 u 1:2:(myColor($3)) w l lc rgb var
### end of script

Result:

Addition: (with OP's data, please reduce for a minimal example.)

I'm still confused. Ok, contour lines all in black, but values above 2000 in red? You could use the ternary operator to map all values >=2000 to the fixed value of 6000 (which will be red).

Script:

### contour lines with custom colors
reset session

FILE = 'TH1TH2.dat'

set pm3d
set contour
unset surface
set cntrparam levels 20

set table $Contour
    splot FILE u 1:2:3
unset table

set palette rgb 33,13,10
set size ratio 1
unset key
set tics out
set xrange[0:180]
set yrange[0:180]

myValue(v) = v>=2000 ? 6000 : v

plot FILE u 1:2:(myValue($3)) w image, \
     $Contour u 1:2 w l lc "black"
### end of script

Result:

Script 2:

### contour lines with custom colors
reset session

FILE = 'TH1TH2.dat'

set pm3d
set contour
unset surface
set cntrparam levels discrete -2000,-1800,-1600,-1400,-1200,-1000,-800,-600,-400-200,0,\
      200,400,600,800,1000,1200,1400,1600,1800,2000

set table $Contour
    splot FILE u 1:2:3 every 10
unset table

set palette rgb 33,13,10
set size ratio 1
unset key
set tics out
set xrange[0:180]
set yrange[0:180]

myValue(v) = v>=2000 ? 6000 : v

plot FILE u 1:2:(myValue($3)) w image, \
     $Contour u 1:2 w l lc "black"
### end of script

Result 2: