The generator matrix

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

generates a code of length 54 over Z5[X]/(X^2) who´s minimum homogenous weight is 207.

Homogenous weight enumerator: w(x)=1x^0+1700x^207+1240x^208+320x^209+32x^210+1960x^212+1820x^213+560x^214+64x^215+1820x^217+1420x^218+320x^219+1280x^222+1140x^223+300x^224+1240x^227+380x^228+12x^230+16x^235

The gray image is a linear code over GF(5) with n=270, k=6 and d=207.
This code was found by Heurico 1.16 in 66.6 seconds.