The generator matrix

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

generates a code of length 27 over Z5[X]/(X^2) who´s minimum homogenous weight is 107.

Homogenous weight enumerator: w(x)=1x^0+240x^107+300x^108+12x^110+60x^112+12x^115

The gray image is a linear code over GF(5) with n=135, k=4 and d=107.
This code was found by Heurico 1.16 in 0.00169 seconds.