The generator matrix

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

generates a code of length 24 over Z5[X]/(X^2) who´s minimum homogenous weight is 83.

Homogenous weight enumerator: w(x)=1x^0+440x^83+100x^84+684x^85+1300x^86+1060x^87+2460x^88+1200x^89+2680x^90+3100x^91+1320x^92+5880x^93+4800x^94+7340x^95+7400x^96+3180x^97+10600x^98+6400x^99+7268x^100+5700x^101+1940x^102+3120x^103+64x^105+60x^110+24x^115+4x^120

The gray image is a linear code over GF(5) with n=120, k=7 and d=83.
This code was found by Heurico 1.16 in 4.6 seconds.