The generator matrix

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

generates a code of length 71 over Z5[X]/(X^2) who´s minimum homogenous weight is 275.

Homogenous weight enumerator: w(x)=1x^0+176x^275+752x^280+2084x^285+28x^300+48x^305+16x^310+16x^325+4x^350

The gray image is a linear code over GF(5) with n=355, k=5 and d=275.
This code was found by Heurico 1.16 in 15 seconds.