The generator matrix

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

generates a code of length 71 over Z5[X]/(X^2) who´s minimum homogenous weight is 279.

Homogenous weight enumerator: w(x)=1x^0+980x^279+312x^280+860x^284+200x^285+440x^289+20x^290+120x^294+80x^295+100x^299+4x^300+4x^305+4x^330

The gray image is a linear code over GF(5) with n=355, k=5 and d=279.
This code was found by Heurico 1.16 in 0.065 seconds.