The generator matrix

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

generates a code of length 23 over Z5[X]/(X^2) who´s minimum homogenous weight is 86.

Homogenous weight enumerator: w(x)=1x^0+240x^86+800x^87+76x^90+320x^91+400x^92+40x^95+440x^96+800x^97+4x^100+4x^115

The gray image is a linear code over GF(5) with n=115, k=5 and d=86.
This code was found by Heurico 1.16 in 0.231 seconds.