The generator matrix

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

generates a code of length 23 over Z5[X]/(X^2) who´s minimum homogenous weight is 77.

Homogenous weight enumerator: w(x)=1x^0+580x^77+1820x^78+1340x^79+364x^80+1900x^81+5480x^82+8800x^83+6560x^84+3760x^85+8700x^86+18080x^87+24680x^88+20180x^89+14552x^90+24900x^91+55080x^92+48960x^93+36100x^94+19296x^95+24500x^96+30780x^97+25740x^98+8320x^99+60x^100+52x^105+16x^110+24x^115

The gray image is a linear code over GF(5) with n=115, k=8 and d=77.
This code was found by Heurico 1.16 in 63.7 seconds.