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

generates a code of length 76 over Z5[X]/(X^2) who´s minimum homogenous weight is 295.

Homogenous weight enumerator: w(x)=1x^0+600x^295+520x^300+1256x^305+640x^310+48x^320+20x^325+16x^330+12x^345+4x^350+8x^355

The gray image is a linear code over GF(5) with n=380, k=5 and d=295.
This code was found by Heurico 1.16 in 18 seconds.