The generator matrix

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

generates a code of length 58 over Z5[X]/(X^2) who´s minimum homogenous weight is 210.

Homogenous weight enumerator: w(x)=1x^0+136x^210+140x^211+484x^215+1540x^216+1216x^220+4880x^221+2092x^225+9740x^226+4012x^230+18440x^231+4568x^235+18900x^236+2332x^240+8300x^241+208x^245+560x^246+240x^250+148x^255+96x^260+64x^265+16x^270+12x^275

The gray image is a linear code over GF(5) with n=290, k=7 and d=210.
This code was found by Heurico 1.16 in 10.7 seconds.