The generator matrix

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

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+720x^90+1056x^95+1344x^100+4x^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 0.00712 seconds.