The generator matrix

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

generates a code of length 71 over Z5[X]/(X^2) who´s minimum homogenous weight is 274.

Homogenous weight enumerator: w(x)=1x^0+1680x^274+772x^275+3780x^279+736x^280+2940x^284+520x^285+1900x^289+560x^290+1360x^294+480x^295+840x^299+32x^300+24x^305

The gray image is a linear code over GF(5) with n=355, k=6 and d=274.
This code was found by Heurico 1.16 in 0.989 seconds.