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

generates a code of length 62 over Z5[X]/(X^2) who´s minimum homogenous weight is 241.

Homogenous weight enumerator: w(x)=1x^0+60x^241+140x^242+880x^243+52x^245+300x^246+220x^247+560x^248+44x^250+80x^251+40x^252+240x^253+8x^255+100x^257+320x^258+16x^260+60x^261+4x^265

The gray image is a linear code over GF(5) with n=310, k=5 and d=241.
This code was found by Heurico 1.16 in 80.7 seconds.