The generator matrix

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

generates a code of length 76 over Z5[X]/(X^2) who´s minimum homogenous weight is 280.

Homogenous weight enumerator: w(x)=1x^0+108x^280+368x^285+456x^290+100x^292+392x^295+1200x^297+352x^300+4800x^302+332x^305+6400x^307+244x^310+236x^315+156x^320+116x^325+136x^330+84x^335+84x^340+32x^345+16x^350+4x^355+4x^360+4x^365

The gray image is a linear code over GF(5) with n=380, k=6 and d=280.
This code was found by Heurico 1.16 in 1.31 seconds.