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

generates a code of length 77 over Z5[X]/(X^2) who´s minimum homogenous weight is 303.

Homogenous weight enumerator: w(x)=1x^0+200x^303+48x^305+100x^308+56x^310+200x^313+12x^315+4x^320+4x^360

The gray image is a linear code over GF(5) with n=385, k=4 and d=303.
This code was found by Heurico 1.16 in 0.179 seconds.