The generator matrix

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

generates a code of length 67 over Z5[X]/(X^2) who´s minimum homogenous weight is 252.

Homogenous weight enumerator: w(x)=1x^0+560x^252+880x^253+1000x^254+712x^255+340x^256+2760x^257+2680x^258+3520x^259+1324x^260+380x^261+5480x^262+4660x^263+3940x^264+1744x^265+500x^266+5140x^267+5280x^268+4600x^269+1896x^270+620x^271+5700x^272+5700x^273+4360x^274+1780x^275+540x^276+4100x^277+2940x^278+2120x^279+576x^280+120x^281+1260x^282+360x^283+460x^284+44x^285+8x^290+16x^295+16x^300+4x^305+4x^310

The gray image is a linear code over GF(5) with n=335, k=7 and d=252.
This code was found by Heurico 1.16 in 14.9 seconds.