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

generates a code of length 66 over Z5[X]/(X^2) who´s minimum homogenous weight is 248.

Homogenous weight enumerator: w(x)=1x^0+860x^248+860x^249+336x^250+580x^251+540x^252+4460x^253+2520x^254+808x^255+1740x^256+1000x^257+7380x^258+4020x^259+1244x^260+2120x^261+1040x^262+7980x^263+4620x^264+1192x^265+2800x^266+1080x^267+8880x^268+4720x^269+1552x^270+2180x^271+1020x^272+6320x^273+2860x^274+400x^275+580x^276+320x^277+1620x^278+400x^279+16x^280+36x^285+12x^290+12x^295+12x^300+4x^310

The gray image is a linear code over GF(5) with n=330, k=7 and d=248.
This code was found by Heurico 1.16 in 10.1 seconds.