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

generates a code of length 55 over Z5[X]/(X^2) who´s minimum homogenous weight is 200.

Homogenous weight enumerator: w(x)=1x^0+240x^200+492x^205+444x^210+348x^215+12860x^220+336x^225+236x^230+228x^235+172x^240+140x^245+84x^250+32x^255+8x^260+4x^275

The gray image is a linear code over GF(5) with n=275, k=6 and d=200.
This code was found by Heurico 1.16 in 0.882 seconds.