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

generates a code of length 97 over Z5[X]/(X^2) who´s minimum homogenous weight is 380.

Homogenous weight enumerator: w(x)=1x^0+172x^380+500x^384+280x^385+2000x^389+52x^390+16x^395+64x^405+20x^410+8x^415+4x^420+4x^425+4x^480

The gray image is a linear code over GF(5) with n=485, k=5 and d=380.
This code was found by Heurico 1.16 in 0.213 seconds.