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

generates a code of length 62 over Z5[X]/(X^2) who´s minimum homogenous weight is 235.

Homogenous weight enumerator: w(x)=1x^0+68x^235+280x^240+928x^245+1696x^250+52x^255+32x^260+12x^265+16x^270+8x^275+12x^280+4x^285+12x^290+4x^300

The gray image is a linear code over GF(5) with n=310, k=5 and d=235.
This code was found by Heurico 1.16 in 0.0698 seconds.