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

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+300x^83+160x^84+676x^85+1700x^86+700x^87+1920x^88+1920x^89+2688x^90+3900x^91+900x^92+2940x^93+7680x^94+7356x^95+9600x^96+2100x^97+4660x^98+10240x^99+7244x^100+7300x^101+1300x^102+2680x^103+80x^105+44x^110+32x^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 11.9 seconds.