The generator matrix

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

generates a code of length 77 over Z5[X]/(X^2) who´s minimum homogenous weight is 287.

Homogenous weight enumerator: w(x)=1x^0+940x^287+880x^288+1700x^289+1676x^290+2300x^291+4900x^292+4680x^293+5060x^294+5460x^295+5200x^296+10920x^297+8360x^298+10720x^299+7664x^300+9020x^301+17760x^302+14980x^303+14980x^304+12112x^305+12480x^306+24060x^307+20360x^308+20680x^309+14876x^310+13300x^311+25160x^312+19360x^313+18580x^314+12400x^315+10320x^316+17740x^317+11740x^318+9020x^319+5508x^320+4140x^321+5160x^322+2140x^323+1760x^324+872x^325+740x^326+860x^327+16x^330+16x^335+16x^340+4x^345+4x^355

The gray image is a linear code over GF(5) with n=385, k=8 and d=287.
This code was found by Heurico 1.16 in 367 seconds.