The generator matrix

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

generates a code of length 24 over Z5[X]/(X^2) who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+84x^70+508x^75+992x^80+1616x^85+2056x^90+12500x^92+2956x^95+50000x^97+3256x^100+2408x^105+1284x^110+384x^115+80x^120

The gray image is a linear code over GF(5) with n=120, k=7 and d=70.
This code was found by Heurico 1.16 in 6.48 seconds.