The generator matrix

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

generates a code of length 55 over Z5[X]/(X^2) who´s minimum homogenous weight is 207.

Homogenous weight enumerator: w(x)=1x^0+400x^207+540x^208+216x^210+1280x^212+1340x^213+112x^215+1680x^217+1960x^218+88x^220+2080x^222+2080x^223+84x^225+1680x^227+1400x^228+24x^230+380x^232+180x^233+36x^235+28x^240+16x^245+4x^250+12x^260+4x^265

The gray image is a linear code over GF(5) with n=275, k=6 and d=207.
This code was found by Heurico 1.16 in 78.3 seconds.