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

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+680x^209+1128x^210+1040x^211+500x^212+1220x^213+3140x^214+3184x^215+1740x^216+1060x^217+1800x^218+5420x^219+5240x^220+3060x^221+1060x^222+2580x^223+7600x^224+5496x^225+2980x^226+1060x^227+2660x^228+7580x^229+5940x^230+2700x^231+960x^232+1640x^233+3080x^234+2052x^235+980x^236+360x^237+100x^238+32x^240+24x^245+12x^250+4x^255+4x^260+8x^265

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 7.91 seconds.