The generator matrix

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

generates a code of length 54 over Z5[X]/(X^2) who´s minimum homogenous weight is 200.

Homogenous weight enumerator: w(x)=1x^0+316x^200+480x^201+540x^202+180x^203+1060x^204+2420x^205+2220x^206+2840x^207+380x^208+2400x^209+5024x^210+4080x^211+4040x^212+700x^213+2920x^214+6712x^215+5640x^216+3940x^217+420x^218+3240x^219+6724x^220+5200x^221+4440x^222+640x^223+2360x^224+4160x^225+2380x^226+1700x^227+180x^228+520x^229+220x^230+12x^235+8x^240+16x^245+8x^250+4x^260

The gray image is a linear code over GF(5) with n=270, k=7 and d=200.
This code was found by Heurico 1.16 in 7.82 seconds.