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

generates a code of length 56 over Z5[X]/(X^2) who´s minimum homogenous weight is 212.

Homogenous weight enumerator: w(x)=1x^0+20x^212+232x^215+240x^217+160x^220+960x^222+56x^225+1280x^227+32x^230+64x^235+32x^240+24x^245+8x^260+8x^265+8x^270

The gray image is a linear code over GF(5) with n=280, k=5 and d=212.
This code was found by Heurico 1.16 in 88.4 seconds.