The generator matrix

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

generates a code of length 75 over Z5[X]/(X^2) who´s minimum homogenous weight is 283.

Homogenous weight enumerator: w(x)=1x^0+560x^283+420x^284+376x^285+460x^286+960x^287+4220x^288+1860x^289+1292x^290+1320x^291+1680x^292+6400x^293+2600x^294+1620x^295+1700x^296+1880x^297+8100x^298+3500x^299+1588x^300+1400x^301+2400x^302+8200x^303+3400x^304+1716x^305+1300x^306+2120x^307+7140x^308+2480x^309+1088x^310+1040x^311+880x^312+2480x^313+740x^314+388x^315+280x^316+80x^317+400x^318+24x^320+4x^325+12x^330+4x^335+4x^340+4x^345+4x^365

The gray image is a linear code over GF(5) with n=375, k=7 and d=283.
This code was found by Heurico 1.16 in 11.5 seconds.