The generator matrix

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

generates a code of length 56 over Z5[X]/(X^2) who´s minimum homogenous weight is 209.

Homogenous weight enumerator: w(x)=1x^0+660x^209+1080x^210+1180x^211+520x^212+440x^213+3540x^214+2824x^215+3160x^216+1040x^217+1160x^218+5980x^219+4316x^220+3840x^221+1060x^222+1080x^223+8220x^224+5376x^225+3920x^226+980x^227+1600x^228+8160x^229+5144x^230+4100x^231+1100x^232+720x^233+3440x^234+1792x^235+1300x^236+300x^237+44x^240+12x^245+20x^250+8x^255+4x^265+4x^270

The gray image is a linear code over GF(5) with n=280, k=7 and d=209.
This code was found by Heurico 1.16 in 8.23 seconds.