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

generates a code of length 76 over Z5[X]/(X^2) who´s minimum homogenous weight is 294.

Homogenous weight enumerator: w(x)=1x^0+840x^294+1456x^295+1020x^296+120x^297+1240x^299+2132x^300+920x^301+160x^302+840x^304+1348x^305+660x^306+120x^307+580x^309+1100x^310+360x^311+100x^312+660x^314+720x^315+420x^316+340x^319+352x^320+120x^321+4x^325+8x^330+4x^340

The gray image is a linear code over GF(5) with n=380, k=6 and d=294.
This code was found by Heurico 1.16 in 25.1 seconds.