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  1  1  1
 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  0 2X+1 3X+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 2X+2 4X+1
 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 3X 2X 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+596x^205+1280x^206+1040x^207+160x^208+260x^209+3720x^210+3760x^211+2620x^212+440x^213+440x^214+6716x^215+5940x^216+3240x^217+520x^218+620x^219+7488x^220+7420x^221+3660x^222+1000x^223+900x^224+8464x^225+6400x^226+3280x^227+380x^228+280x^229+3536x^230+2700x^231+1160x^232+32x^235+36x^240+20x^245+12x^250+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 7.92 seconds.