The generator matrix

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

generates a code of length 17 over Z5[X]/(X^2) who´s minimum homogenous weight is 55.

Homogenous weight enumerator: w(x)=1x^0+48x^55+156x^60+500x^64+108x^65+2000x^69+108x^70+112x^75+60x^80+32x^85

The gray image is a linear code over GF(5) with n=85, k=5 and d=55.
This code was found by Heurico 1.16 in 0.00887 seconds.