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

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+160x^210+408x^215+536x^220+1584x^225+5160x^230+6700x^235+296x^240+228x^245+228x^250+140x^255+100x^260+56x^265+16x^270+12x^275

The gray image is a linear code over GF(5) with n=290, k=6 and d=210.
This code was found by Heurico 1.16 in 0.94 seconds.