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

generates a code of length 75 over Z5[X]/(X^2) who´s minimum homogenous weight is 290.

Homogenous weight enumerator: w(x)=1x^0+2600x^290+4120x^295+3432x^300+2620x^305+1820x^310+1020x^315+12x^325

The gray image is a linear code over GF(5) with n=375, k=6 and d=290.
This code was found by Heurico 1.16 in 5.56 seconds.