The generator matrix

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

generates a code of length 20 over Z5[X]/(X^2) who´s minimum homogenous weight is 55.

Homogenous weight enumerator: w(x)=1x^0+96x^55+484x^60+940x^65+1588x^70+2448x^75+12500x^76+3544x^80+50000x^81+3376x^85+2120x^90+852x^95+176x^100

The gray image is a linear code over GF(5) with n=100, k=7 and d=55.
This code was found by Heurico 1.16 in 4.64 seconds.