The generator matrix

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

generates a code of length 55 over Z5[X]/(X^2) who´s minimum homogenous weight is 205.

Homogenous weight enumerator: w(x)=1x^0+672x^205+1200x^206+880x^207+120x^208+440x^209+3580x^210+3900x^211+2580x^212+480x^213+460x^214+6600x^215+6140x^216+3460x^217+640x^218+400x^219+7864x^220+6780x^221+3840x^222+800x^223+640x^224+8252x^225+6920x^226+3220x^227+460x^228+480x^229+3548x^230+2560x^231+1020x^232+80x^234+44x^235+24x^240+16x^245+16x^250+4x^255+4x^270

The gray image is a linear code over GF(5) with n=275, k=7 and d=205.
This code was found by Heurico 1.16 in 8.25 seconds.