The generator matrix

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

generates a code of length 81 over Z5[X]/(X^2) who´s minimum homogenous weight is 302.

Homogenous weight enumerator: w(x)=1x^0+340x^302+1420x^303+660x^304+820x^305+2580x^306+3540x^307+5880x^308+3820x^309+3112x^310+6520x^311+7160x^312+12240x^313+7420x^314+5800x^315+10680x^316+11980x^317+18440x^318+12340x^319+8472x^320+15180x^321+16880x^322+25680x^323+16220x^324+11280x^325+19900x^326+18280x^327+26720x^328+15280x^329+9932x^330+16840x^331+14520x^332+19220x^333+9340x^334+5072x^335+7320x^336+6240x^337+7020x^338+2360x^339+1064x^340+980x^341+1060x^342+880x^343+60x^344+36x^345+12x^350+16x^355+4x^360+4x^365

The gray image is a linear code over GF(5) with n=405, k=8 and d=302.
This code was found by Heurico 1.16 in 328 seconds.