The generator matrix

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

generates a code of length 18 over Z5[X]/(X^2) who´s minimum homogenous weight is 55.

Homogenous weight enumerator: w(x)=1x^0+132x^55+400x^60+424x^65+520x^70+12500x^72+744x^75+608x^80+260x^85+36x^90

The gray image is a linear code over GF(5) with n=90, k=6 and d=55.
This code was found by Heurico 1.16 in 0.193 seconds.