The generator matrix

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

generates a code of length 75 over Z5[X]/(X^2) who´s minimum homogenous weight is 284.

Homogenous weight enumerator: w(x)=1x^0+660x^284+1608x^285+840x^286+440x^287+280x^288+2660x^289+4388x^290+2200x^291+1520x^292+460x^293+4180x^294+7440x^295+2580x^296+1560x^297+560x^298+5400x^299+6828x^300+2520x^301+1600x^302+560x^303+4520x^304+6412x^305+2260x^306+1840x^307+460x^308+3780x^309+4816x^310+1560x^311+540x^312+180x^313+1300x^314+1568x^315+540x^316+20x^320+16x^325+8x^330+16x^335+4x^340

The gray image is a linear code over GF(5) with n=375, k=7 and d=284.
This code was found by Heurico 1.16 in 40.2 seconds.