The generator matrix

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

generates a code of length 56 over Z5[X]/(X^2) who´s minimum homogenous weight is 204.

Homogenous weight enumerator: w(x)=1x^0+540x^204+592x^205+860x^206+1260x^207+3120x^208+3280x^209+3548x^210+4180x^211+4720x^212+8920x^213+7320x^214+8348x^215+9980x^216+9060x^217+15760x^218+15920x^219+16196x^220+17120x^221+14000x^222+25980x^223+24880x^224+22132x^225+20460x^226+17740x^227+27400x^228+24100x^229+18972x^230+15740x^231+11120x^232+13900x^233+8420x^234+5760x^235+4160x^236+2100x^237+2420x^238+540x^239+28x^240+20x^245+8x^250+12x^255+8x^260

The gray image is a linear code over GF(5) with n=280, k=8 and d=204.
This code was found by Heurico 1.16 in 194 seconds.