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

generates a code of length 55 over Z5[X]/(X^2) who´s minimum homogenous weight is 210.

Homogenous weight enumerator: w(x)=1x^0+188x^210+160x^215+500x^216+88x^220+2000x^221+56x^225+36x^230+32x^235+24x^240+12x^245+12x^250+8x^255+4x^260+4x^270

The gray image is a linear code over GF(5) with n=275, k=5 and d=210.
This code was found by Heurico 1.16 in 0.681 seconds.