The generator matrix

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

generates a code of length 79 over Z5[X]/(X^2) who´s minimum homogenous weight is 295.

Homogenous weight enumerator: w(x)=1x^0+1256x^295+1140x^296+1420x^297+1580x^298+3180x^299+5368x^300+4300x^301+4640x^302+3980x^303+7060x^304+12836x^305+7480x^306+8680x^307+6200x^308+10640x^309+19948x^310+12780x^311+14020x^312+9700x^313+15100x^314+28872x^315+17740x^316+18680x^317+11280x^318+16820x^319+30984x^320+16080x^321+15320x^322+8980x^323+13360x^324+18920x^325+10000x^326+8060x^327+4960x^328+5600x^329+6740x^330+2800x^331+1680x^332+820x^333+740x^334+648x^335+180x^336+24x^340+16x^345+12x^350

The gray image is a linear code over GF(5) with n=395, k=8 and d=295.
This code was found by Heurico 1.16 in 332 seconds.