The generator matrix

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

generates a code of length 52 over Z5[X]/(X^2) who´s minimum homogenous weight is 199.

Homogenous weight enumerator: w(x)=1x^0+2140x^199+772x^200+3380x^204+784x^205+3120x^209+660x^210+2560x^214+740x^215+1300x^219+140x^220+12x^225+16x^230

The gray image is a linear code over GF(5) with n=260, k=6 and d=199.
This code was found by Heurico 1.16 in 14.3 seconds.