The generator matrix

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

generates a code of length 53 over Z5[X]/(X^2) who´s minimum homogenous weight is 197.

Homogenous weight enumerator: w(x)=1x^0+400x^197+960x^198+1440x^199+444x^200+540x^201+2300x^202+3240x^203+4240x^204+924x^205+860x^206+4400x^207+4880x^208+5280x^209+1456x^210+1380x^211+5000x^212+5820x^213+7320x^214+1780x^215+1500x^216+5600x^217+5460x^218+5360x^219+916x^220+720x^221+2300x^222+2140x^223+1360x^224+28x^225+40x^230+8x^235+8x^240+12x^245+4x^255+4x^260

The gray image is a linear code over GF(5) with n=265, k=7 and d=197.
This code was found by Heurico 1.16 in 7.82 seconds.