The generator matrix

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

generates a code of length 57 over Z5[X]/(X^2) who´s minimum homogenous weight is 212.

Homogenous weight enumerator: w(x)=1x^0+500x^212+380x^213+640x^214+288x^215+900x^216+3580x^217+2040x^218+2120x^219+560x^220+1740x^221+6080x^222+3580x^223+3400x^224+704x^225+2240x^226+8080x^227+4720x^228+3680x^229+624x^230+3040x^231+8280x^232+4760x^233+3760x^234+592x^235+1740x^236+4980x^237+2020x^238+1400x^239+280x^240+340x^241+1000x^242+28x^245+24x^250+4x^255+16x^260+4x^275

The gray image is a linear code over GF(5) with n=285, k=7 and d=212.
This code was found by Heurico 1.16 in 8.68 seconds.