The generator matrix

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

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+292x^200+160x^201+20x^202+240x^203+848x^205+1380x^206+520x^207+1280x^208+1600x^210+2660x^211+1220x^212+3580x^213+2840x^215+5060x^216+3520x^217+7180x^218+4008x^220+7660x^221+4620x^222+8580x^223+3888x^225+6000x^226+2600x^227+4140x^228+1484x^230+2080x^231+188x^235+216x^240+132x^245+64x^250+48x^255+12x^260+4x^265

The gray image is a linear code over GF(5) with n=275, k=7 and d=200.
This code was found by Heurico 1.16 in 11.7 seconds.