The generator matrix

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

generates a code of length 24 over Z5[X]/(X^2) who´s minimum homogenous weight is 81.

Homogenous weight enumerator: w(x)=1x^0+420x^81+1860x^82+2200x^83+180x^84+2080x^85+4900x^86+9440x^87+9220x^88+2160x^89+9228x^90+13780x^91+27020x^92+27040x^93+8640x^94+26064x^95+41060x^96+57200x^97+45960x^98+11520x^99+25620x^100+24840x^101+26980x^102+13080x^103+36x^105+56x^110+28x^115+12x^120

The gray image is a linear code over GF(5) with n=120, k=8 and d=81.
This code was found by Heurico 1.16 in 66.1 seconds.