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

generates a code of length 66 over Z5[X]/(X^2) who´s minimum homogenous weight is 244.

Homogenous weight enumerator: w(x)=1x^0+1140x^244+1724x^245+1000x^246+880x^247+2420x^248+6000x^249+6912x^250+3500x^251+2600x^252+6780x^253+12880x^254+13392x^255+6480x^256+5460x^257+12020x^258+21500x^259+22136x^260+9800x^261+8900x^262+18600x^263+32100x^264+29788x^265+12600x^266+8740x^267+19980x^268+30460x^269+26568x^270+10300x^271+6700x^272+10740x^273+15900x^274+10552x^275+3500x^276+1720x^277+1960x^278+2520x^279+1980x^280+320x^281+40x^285+8x^290+4x^295+16x^300+4x^305

The gray image is a linear code over GF(5) with n=330, k=8 and d=244.
This code was found by Heurico 1.16 in 255 seconds.