The generator matrix

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

generates a code of length 53 over Z5[X]/(X^2) who´s minimum homogenous weight is 206.

Homogenous weight enumerator: w(x)=1x^0+280x^206+840x^207+64x^210+440x^211+580x^212+44x^215+80x^216+320x^217+12x^220+200x^221+260x^222+4x^240

The gray image is a linear code over GF(5) with n=265, k=5 and d=206.
This code was found by Heurico 1.16 in 0.03 seconds.