The generator matrix

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

generates a code of length 19 over Z5[X]/(X^2) who´s minimum homogenous weight is 55.

Homogenous weight enumerator: w(x)=1x^0+400x^55+876x^60+1276x^65+2460x^70+3324x^75+62500x^76+3680x^80+2384x^85+964x^90+260x^95

The gray image is a linear code over GF(5) with n=95, k=7 and d=55.
This code was found by Heurico 1.16 in 8.7 seconds.