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

generates a code of length 58 over Z5[X]/(X^2) who´s minimum homogenous weight is 200.

Homogenous weight enumerator: w(x)=1x^0+188x^200+704x^205+892x^210+1240x^215+1996x^220+7524x^225+25820x^230+33768x^235+1876x^240+1588x^245+1160x^250+732x^255+380x^260+184x^265+56x^270+12x^275+4x^280

The gray image is a linear code over GF(5) with n=290, k=7 and d=200.
This code was found by Heurico 1.16 in 22.8 seconds.