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

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+700x^252+720x^253+1140x^254+916x^255+3160x^257+2300x^258+2720x^259+2480x^260+5600x^262+3540x^263+4380x^264+2768x^265+5660x^267+4220x^268+4980x^269+3088x^270+6420x^272+3800x^273+4480x^274+2688x^275+4780x^277+2260x^278+2140x^279+1092x^280+1180x^282+660x^283+160x^284+12x^285+44x^290+24x^295+8x^300+4x^305

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 11.7 seconds.