The generator matrix

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

generates a code of length 67 over Z5[X]/(X^2) who´s minimum homogenous weight is 248.

Homogenous weight enumerator: w(x)=1x^0+1120x^248+1820x^249+1256x^250+1140x^251+2560x^252+5600x^253+7260x^254+3708x^255+3460x^256+5620x^257+11840x^258+13000x^259+7696x^260+7400x^261+10300x^262+20800x^263+22220x^264+10672x^265+12440x^266+15380x^267+27660x^268+28400x^269+14308x^270+14980x^271+17460x^272+27900x^273+26560x^274+10644x^275+8980x^276+9280x^277+14880x^278+11500x^279+4252x^280+1600x^281+1900x^282+2700x^283+1740x^284+524x^285+28x^290+32x^295+4x^300

The gray image is a linear code over GF(5) with n=335, k=8 and d=248.
This code was found by Heurico 1.16 in 260 seconds.