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

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+820x^248+780x^249+392x^250+300x^251+740x^252+4200x^253+3640x^254+740x^255+920x^256+1340x^257+6700x^258+4880x^259+1132x^260+1240x^261+1700x^262+7440x^263+5780x^264+1404x^265+960x^266+1860x^267+8680x^268+6080x^269+1448x^270+1180x^271+1620x^272+5600x^273+3100x^274+412x^275+400x^276+240x^277+1560x^278+740x^279+32x^280+16x^285+28x^290+4x^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 10.7 seconds.