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

generates a code of length 59 over Z5[X]/(X^2) who´s minimum homogenous weight is 225.

Homogenous weight enumerator: w(x)=1x^0+120x^225+100x^228+212x^230+800x^233+88x^235+1600x^238+64x^240+56x^245+20x^250+16x^255+16x^260+4x^265+12x^270+12x^275+4x^285

The gray image is a linear code over GF(5) with n=295, k=5 and d=225.
This code was found by Heurico 1.16 in 0.0628 seconds.