The generator matrix

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

generates a code of length 54 over Z5[X]/(X^2) who´s minimum homogenous weight is 204.

Homogenous weight enumerator: w(x)=1x^0+500x^204+152x^205+1040x^206+1540x^209+156x^210+1400x^211+1620x^214+92x^215+2060x^216+2300x^219+88x^220+2520x^221+1380x^224+40x^225+480x^226+160x^229+36x^230+12x^235+24x^240+8x^245+8x^255+8x^260

The gray image is a linear code over GF(5) with n=270, k=6 and d=204.
This code was found by Heurico 1.16 in 2.32 seconds.