The generator matrix

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

generates a code of length 62 over Z5[X]/(X^2) who´s minimum homogenous weight is 240.

Homogenous weight enumerator: w(x)=1x^0+24x^240+60x^241+200x^243+1120x^244+24x^245+300x^246+100x^248+480x^249+28x^250+60x^251+200x^253+80x^254+44x^255+40x^256+320x^259+40x^261+4x^285

The gray image is a linear code over GF(5) with n=310, k=5 and d=240.
This code was found by Heurico 1.16 in 0.0455 seconds.