The generator matrix

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

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+32x^55+60x^56+80x^57+344x^60+720x^61+360x^62+1752x^65+2880x^66+1040x^67+3312x^70+3840x^71+1020x^72+96x^75+60x^80+28x^85

The gray image is a linear code over GF(5) with n=85, k=6 and d=55.
This code was found by Heurico 1.16 in 0.0894 seconds.