The generator matrix

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

generates a code of length 57 over Z5[X]/(X^2) who´s minimum homogenous weight is 222.

Homogenous weight enumerator: w(x)=1x^0+420x^222+640x^223+48x^225+660x^227+480x^228+48x^230+120x^232+120x^233+12x^235+300x^237+260x^238+16x^240

The gray image is a linear code over GF(5) with n=285, k=5 and d=222.
This code was found by Heurico 1.16 in 23.5 seconds.