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

generates a code of length 62 over Z5[X]/(X^2) who´s minimum homogenous weight is 225.

Homogenous weight enumerator: w(x)=1x^0+100x^225+384x^230+472x^235+920x^240+4316x^245+8352x^250+224x^255+212x^260+232x^265+180x^270+128x^275+52x^280+36x^285+8x^290+4x^295+4x^300

The gray image is a linear code over GF(5) with n=310, k=6 and d=225.
This code was found by Heurico 1.16 in 1.02 seconds.