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

generates a code of length 79 over Z5[X]/(X^2) who´s minimum homogenous weight is 305.

Homogenous weight enumerator: w(x)=1x^0+144x^305+148x^310+500x^312+128x^315+2000x^317+72x^320+48x^325+28x^330+16x^335+20x^345+8x^350+8x^360+4x^390

The gray image is a linear code over GF(5) with n=395, k=5 and d=305.
This code was found by Heurico 1.16 in 0.122 seconds.