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

generates a code of length 77 over Z5[X]/(X^2) who´s minimum homogenous weight is 302.

Homogenous weight enumerator: w(x)=1x^0+380x^302+620x^303+44x^305+800x^307+560x^308+56x^310+120x^312+100x^313+12x^315+40x^317+140x^318+4x^320+160x^322+80x^323+4x^330+4x^335

The gray image is a linear code over GF(5) with n=385, k=5 and d=302.
This code was found by Heurico 1.16 in 13.4 seconds.