The generator matrix

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

generates a code of length 71 over Z5[X]/(X^2) who´s minimum homogenous weight is 268.

Homogenous weight enumerator: w(x)=1x^0+1020x^268+880x^269+504x^270+360x^271+580x^272+5120x^273+2280x^274+1284x^275+840x^276+920x^277+8680x^278+3380x^279+1528x^280+1080x^281+1040x^282+8920x^283+4140x^284+2100x^285+1320x^286+1160x^287+9360x^288+3800x^289+1740x^290+960x^291+980x^292+7080x^293+2280x^294+776x^295+440x^296+320x^297+2320x^298+740x^299+124x^300+24x^305+12x^310+12x^315+12x^320+8x^325

The gray image is a linear code over GF(5) with n=355, k=7 and d=268.
This code was found by Heurico 1.16 in 13.3 seconds.