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

generates a code of length 57 over Z5[X]/(X^2) who´s minimum homogenous weight is 215.

Homogenous weight enumerator: w(x)=1x^0+64x^215+180x^220+128x^225+2500x^228+92x^230+60x^235+32x^240+12x^245+12x^250+24x^255+12x^260+4x^270+4x^285

The gray image is a linear code over GF(5) with n=285, k=5 and d=215.
This code was found by Heurico 1.16 in 0.0588 seconds.