The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  X  1  1  1  1  1  1
 0  X  0  0  0  0  0  X  X 4X 2X 3X 4X  X 3X  0  0 4X  X  X  X  X 2X 4X 2X  0 4X  X 3X  X  0  X 3X 3X  0 4X 3X  X 2X 3X 2X 2X 4X 3X  0  0  X 2X  X  X 4X 2X 3X 2X 2X  0
 0  0  X  0  0  X  X 3X 4X 3X  0  X 2X 4X 4X 4X  0 4X 2X 3X  X 4X 2X  0 3X  0  0 2X 4X 4X 2X  X 2X  0 4X  0 3X 4X 4X  X 2X  0  X 3X 3X 2X  X  0 4X  0 2X 2X 2X  X 4X  0
 0  0  0  X  0 3X 2X 3X  X  X 4X  X  0 3X 2X  X 2X 3X  0 4X  0 4X  X  0 3X 2X  X 3X  X 4X 3X  0  X 2X 3X 3X 4X  X  X 2X 4X 3X 3X 4X 2X  0  0 4X 3X  X 4X  X 3X  X 4X  0
 0  0  0  0  X 3X  X 4X 3X  X 3X 4X 2X  0  0  X 3X 3X 4X 3X  0 3X 2X 3X 3X  X 4X 2X 3X  0  0  X  0  X  0 2X  X  X  0 4X 3X 3X 4X 2X 4X  0 2X 4X 3X 2X  0 3X 4X 4X  X  X

generates a code of length 56 over Z5[X]/(X^2) who´s minimum homogenous weight is 200.

Homogenous weight enumerator: w(x)=1x^0+88x^200+288x^205+468x^210+376x^215+500x^216+324x^220+4000x^221+360x^225+8000x^226+388x^230+244x^235+208x^240+132x^245+116x^250+64x^255+48x^260+16x^265+4x^270

The gray image is a linear code over GF(5) with n=280, k=6 and d=200.
This code was found by Heurico 1.16 in 0.891 seconds.