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

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+1600x^298+1280x^299+104x^300+2820x^303+1160x^304+220x^305+2120x^308+1000x^309+168x^310+1560x^313+760x^314+60x^315+1240x^318+440x^319+60x^320+660x^323+360x^324+12x^335

The gray image is a linear code over GF(5) with n=385, k=6 and d=298.
This code was found by Heurico 1.16 in 0.564 seconds.