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

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+880x^268+1220x^269+500x^270+220x^271+760x^272+4320x^273+3180x^274+880x^275+840x^276+1600x^277+6620x^278+5020x^279+1160x^280+1120x^281+1500x^282+8020x^283+5600x^284+1112x^285+1500x^286+1700x^287+7520x^288+5780x^289+1016x^290+1180x^291+1400x^292+5540x^293+3340x^294+700x^295+140x^296+540x^297+2100x^298+860x^299+180x^300+40x^305+12x^310+8x^315+4x^320+8x^325+4x^330

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 11.7 seconds.