The generator matrix

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

generates a code of length 62 over Z5[X]/(X^2) who´s minimum homogenous weight is 232.

Homogenous weight enumerator: w(x)=1x^0+680x^232+560x^233+660x^234+624x^235+460x^236+3600x^237+2280x^238+2620x^239+1416x^240+820x^241+5260x^242+3640x^243+3980x^244+1916x^245+1200x^246+6940x^247+4000x^248+4240x^249+1656x^250+1480x^251+7620x^252+4460x^253+4300x^254+1816x^255+860x^256+4820x^257+2260x^258+1700x^259+616x^260+180x^261+1080x^262+300x^263+20x^265+28x^270+12x^275+8x^280+4x^285+8x^290

The gray image is a linear code over GF(5) with n=310, k=7 and d=232.
This code was found by Heurico 1.16 in 9.14 seconds.