The generator matrix

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

generates a code of length 62 over Z5[X]/(X^2) who´s minimum homogenous weight is 237.

Homogenous weight enumerator: w(x)=1x^0+460x^237+360x^238+640x^239+556x^240+740x^241+1880x^242+380x^243+760x^244+500x^245+780x^246+1320x^247+460x^248+640x^249+516x^250+440x^251+1080x^252+500x^253+480x^254+304x^255+320x^256+860x^257+300x^258+480x^259+236x^260+220x^261+400x^262+12x^265

The gray image is a linear code over GF(5) with n=310, k=6 and d=237.
This code was found by Heurico 1.16 in 0.371 seconds.