The generator matrix

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

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+40x^55+240x^56+520x^57+360x^58+720x^59+952x^60+2880x^61+2640x^62+920x^63+840x^64+6512x^65+11520x^66+7160x^67+2080x^68+2160x^69+12912x^70+15360x^71+7180x^72+1640x^73+1280x^74+136x^75+52x^80+20x^85

The gray image is a linear code over GF(5) with n=85, k=7 and d=55.
This code was found by Heurico 1.16 in 1.59 seconds.