The generator matrix

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

generates a code of length 56 over Z5[X]/(X^2) who´s minimum homogenous weight is 210.

Homogenous weight enumerator: w(x)=1x^0+176x^210+140x^211+820x^214+1036x^215+820x^216+1060x^219+1340x^220+900x^221+900x^224+960x^225+2180x^226+1740x^229+1596x^230+960x^231+480x^234+432x^235+24x^240+28x^245+8x^250+12x^255+8x^265+4x^275

The gray image is a linear code over GF(5) with n=280, k=6 and d=210.
This code was found by Heurico 1.16 in 0.407 seconds.