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  1
 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  2  4 3X+3 4X+2
 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 X+3 3X 3X+2 3X+4
 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 4X X+3 X+1 X+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+580x^81+1620x^82+2300x^83+340x^84+1520x^85+5700x^86+9040x^87+8280x^88+4080x^89+6696x^90+17420x^91+25660x^92+21560x^93+16320x^94+18812x^95+50740x^96+56080x^97+34840x^98+21760x^99+18452x^100+30560x^101+25100x^102+13020x^103+68x^105+28x^110+32x^115+16x^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 65.8 seconds.