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

generates a code of length 50 over Z5[X]/(X^2) who´s minimum homogenous weight is 190.

Homogenous weight enumerator: w(x)=1x^0+196x^190+152x^195+500x^196+76x^200+2000x^201+84x^205+28x^210+16x^215+20x^220+24x^225+12x^230+8x^235+4x^240+4x^245

The gray image is a linear code over GF(5) with n=250, k=5 and d=190.
This code was found by Heurico 1.16 in 0.0462 seconds.