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

generates a code of length 77 over Z5[X]/(X^2) who´s minimum homogenous weight is 298.

Homogenous weight enumerator: w(x)=1x^0+200x^298+176x^300+400x^303+276x^305+1100x^308+92x^310+800x^313+32x^325+12x^330+4x^335+16x^350+12x^355+4x^360

The gray image is a linear code over GF(5) with n=385, k=5 and d=298.
This code was found by Heurico 1.16 in 37.5 seconds.