The generator matrix

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

generates a code of length 56 over Z5[X]/(X^2) who´s minimum homogenous weight is 215.

Homogenous weight enumerator: w(x)=1x^0+2720x^215+4560x^220+3520x^225+2740x^230+2080x^235+4x^250

The gray image is a linear code over GF(5) with n=280, k=6 and d=215.
This code was found by Heurico 1.16 in 11.6 seconds.