Hello Masamichi,
Sorry for my late reply!
I checked errata for i.MX6SX( see document "IMX6SXCE.pdf"), There are no errors clarified on Fast boot with DDR mode in it, so Fast boot with DDR mode should be supported by i.MX6SX.
I configured boot selection according to i.MX6SX EVK board, see following, please!
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BOOT_CFG1[7:6] = 01 LCD1_DATA7=0 LCD1_DATA6=1 boot from uSHDC
BOOT_CFG1[5] = 1 LCD1_DATA5 = 1 MMC protocal
BOOT_CFG1[4] = 1 LCD1_DATA4 = 1 Fast boot mode
BOOT_CFG1[3:2]=x0 LCD1_DATA3 = x LCD1_DATA2 = 0 Fast boot ACK enable
BOOT_CFG1[1] = 1 LCD1_DATA1 = 1 eMMC reset enabled via the SD_RST pad
BOOT_CFG1[0] = 0 LCD1_DATA0 = 0 Through the SD pad
BOOT_CFG2[7:5] = 110 LCD1_DATA15=1 LCD1_DATA14=1 LCD1_DATA13=0 8bit DDR mode
BOOT_CFG2[4:3] =11 LCD1_DATA12 = 1 LCD1_DATA11=1 Boot from uSDHC-4 port
BOOT_CFG2[2] = 0 LCD1_DATA10 = 0 BOOT cpu /ddr Frequecy 792/400 MHz
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In additon, see Table 8-18. MMC and eMMC boot details (continued) of reference manual.

In the list, Fast boot and DDR mode are described clearly!
Please let customer try above! If there still exsit issues, I will confirm it with i.MX Expert team!
Have a nice day!
Best Regards,
Weidong