matplot
Change the xlim= for your plot.
set.seed(42)
dat <- setNames(as.data.frame(as.list(runif(10))), seq(4000, 3955, by=-5))
rownames(dat) <- "SOG130123"
dat
#               4000      3995      3990      3985      3980      3975      3970      3965      3960      3955
# SOG130123 0.914806 0.9370754 0.2861395 0.8304476 0.6417455 0.5190959 0.7365883 0.1346666 0.6569923 0.7050648
matplot(as.numeric(colnames(dat)), t(dat), type = "l")

matplot(as.numeric(colnames(dat)), t(dat), type = "l", xlim = c(4000, 3955))

ggplot2
More data:
set.seed(42)
dat <- setNames(data.frame(matrix(runif(30), ncol=10)), seq(4000, 3955, by=-5))
rownames(dat) <- c("SOG130123", "SOG130124", "SOG130125")
dat
#                4000      3995      3990      3985      3980      3975      3970      3965       3960      3955
# SOG130123 0.9148060 0.8304476 0.7365883 0.7050648 0.9346722 0.9400145 0.4749971 0.1387102 0.08243756 0.9057381
# SOG130124 0.9370754 0.6417455 0.1346666 0.4577418 0.2554288 0.9782264 0.5603327 0.9888917 0.51421178 0.4469696
# SOG130125 0.2861395 0.5190959 0.6569923 0.7191123 0.4622928 0.1174874 0.9040314 0.9466682 0.39020347 0.8360043
Reshape and plot:
library(dplyr)
# library(tibble) # rownames_to_column
library(tidyr) # pivot_longer
library(ggplot2)
dat %>%
  tibble::rownames_to_column() %>%
  pivot_longer(-rowname, names_to = "x", values_to = "y") %>%
  mutate(x = as.numeric(x)) %>%
  ggplot(aes(x, y)) +
  geom_line(aes(group = rowname, color = rowname)) +
  scale_x_reverse()

dplyr is not required to do this, nor is tibble, but they make it fairly simple to get things started. For reshaping data to support this, ggplot2 really wants "long" data, and the two best tools to support that are tidyr::pivot_longer and reshape2::melt (and data.table::melt, nearly the same except for using data.table instead of a data.frame for data).