The generator matrix

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

generates a code of length 24 over Z5[X]/(X^2) who´s minimum homogenous weight is 87.

Homogenous weight enumerator: w(x)=1x^0+600x^87+40x^88+360x^89+752x^90+720x^91+2140x^92+320x^93+1080x^94+1016x^95+560x^96+1720x^97+640x^98+1560x^99+1324x^100+720x^101+2040x^102+24x^105+8x^110

The gray image is a linear code over GF(5) with n=120, k=6 and d=87.
This code was found by Heurico 1.16 in 0.118 seconds.