The generator matrix

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

generates a code of length 68 over Z5[X]/(X^2) who´s minimum homogenous weight is 252.

Homogenous weight enumerator: w(x)=1x^0+1180x^252+1760x^253+1640x^254+996x^255+1620x^256+6380x^257+6760x^258+4760x^259+2972x^260+4220x^261+13660x^262+13360x^263+9400x^264+6104x^265+8420x^266+21720x^267+22020x^268+15840x^269+8768x^270+12000x^271+29600x^272+27100x^273+20700x^274+10152x^275+12480x^276+30500x^277+25920x^278+14320x^279+7388x^280+7540x^281+15980x^282+11100x^283+5360x^284+1664x^285+1220x^286+3480x^287+1980x^288+480x^289+28x^290+28x^295+8x^300+12x^305+4x^315

The gray image is a linear code over GF(5) with n=340, k=8 and d=252.
This code was found by Heurico 1.16 in 264 seconds.