The generator matrix

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

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+56x^200+40x^203+60x^204+304x^205+200x^206+340x^208+900x^209+696x^210+880x^211+2040x^213+2340x^214+1400x^215+1520x^216+4140x^218+4440x^219+3424x^220+2820x^221+7340x^223+7740x^224+5316x^225+3620x^226+7800x^228+6980x^229+3548x^230+2620x^231+3300x^233+2540x^234+264x^235+840x^236+204x^240+196x^245+92x^250+88x^255+20x^260+16x^265

The gray image is a linear code over GF(5) with n=280, k=7 and d=200.
This code was found by Heurico 1.16 in 10.3 seconds.