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

generates a code of length 71 over Z5[X]/(X^2) who´s minimum homogenous weight is 250.

Homogenous weight enumerator: w(x)=1x^0+216x^250+596x^255+992x^260+1204x^265+100x^268+1328x^270+1600x^273+1328x^275+9600x^278+1580x^280+25600x^283+1656x^285+25600x^288+1612x^290+1524x^295+1316x^300+948x^305+748x^310+284x^315+188x^320+84x^325+16x^330+4x^335

The gray image is a linear code over GF(5) with n=355, k=7 and d=250.
This code was found by Heurico 1.16 in 29.1 seconds.