The generator matrix

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

generates a code of length 56 over Z5[X]/(X^2) who´s minimum homogenous weight is 190.

Homogenous weight enumerator: w(x)=1x^0+72x^190+440x^195+916x^200+1220x^205+1276x^210+1532x^215+2500x^216+1608x^220+20000x^221+1780x^225+40000x^226+1760x^230+1788x^235+1468x^240+964x^245+508x^250+180x^255+96x^260+8x^265+8x^270

The gray image is a linear code over GF(5) with n=280, k=7 and d=190.
This code was found by Heurico 1.16 in 21.5 seconds.