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

generates a code of length 24 over Z5[X]/(X^2) who´s minimum homogenous weight is 90.

Homogenous weight enumerator: w(x)=1x^0+304x^90+192x^95+2500x^96+24x^100+96x^115+8x^120

The gray image is a linear code over GF(5) with n=120, k=5 and d=90.
This code was found by Heurico 1.16 in 51.5 seconds.