The generator matrix

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

generates a code of length 76 over Z5[X]/(X^2) who´s minimum homogenous weight is 293.

Homogenous weight enumerator: w(x)=1x^0+400x^293+1060x^294+884x^295+240x^296+280x^297+1060x^298+1660x^299+1108x^300+320x^301+340x^302+640x^303+1160x^304+788x^305+180x^306+180x^307+600x^308+1060x^309+768x^310+140x^311+100x^312+440x^313+460x^314+388x^315+100x^316+100x^317+360x^318+600x^319+184x^320+20x^321+4x^325

The gray image is a linear code over GF(5) with n=380, k=6 and d=293.
This code was found by Heurico 1.16 in 0.483 seconds.