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

generates a code of length 75 over Z5[X]/(X^2) who´s minimum homogenous weight is 290.

Homogenous weight enumerator: w(x)=1x^0+200x^290+300x^291+144x^295+500x^296+88x^300+1100x^301+80x^305+600x^306+16x^310+32x^315+20x^320+8x^325+16x^330+4x^340+12x^345+4x^350

The gray image is a linear code over GF(5) with n=375, k=5 and d=290.
This code was found by Heurico 1.16 in 0.109 seconds.