The generator matrix

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

generates a code of length 55 over Z5[X]/(X^2) who´s minimum homogenous weight is 214.

Homogenous weight enumerator: w(x)=1x^0+140x^214+836x^215+280x^216+220x^219+712x^220+120x^221+40x^224+288x^225+20x^226+100x^229+284x^230+80x^231+4x^250

The gray image is a linear code over GF(5) with n=275, k=5 and d=214.
This code was found by Heurico 1.16 in 0.0333 seconds.