The generator matrix

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

generates a code of length 52 over Z5[X]/(X^2) who´s minimum homogenous weight is 193.

Homogenous weight enumerator: w(x)=1x^0+860x^193+700x^194+928x^195+160x^196+800x^197+4400x^198+2380x^199+2076x^200+360x^201+1320x^202+7460x^203+3700x^204+2948x^205+760x^206+2040x^207+10220x^208+4920x^209+3712x^210+760x^211+2260x^212+10280x^213+4540x^214+2476x^215+460x^216+1080x^217+4280x^218+1260x^219+892x^220+32x^225+20x^230+16x^235+12x^240+8x^245+4x^250

The gray image is a linear code over GF(5) with n=260, k=7 and d=193.
This code was found by Heurico 1.16 in 7.77 seconds.