The generator matrix

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

generates a code of length 54 over Z5[X]/(X^2) who´s minimum homogenous weight is 195.

Homogenous weight enumerator: w(x)=1x^0+216x^195+388x^200+436x^205+404x^210+368x^215+12500x^216+288x^220+332x^225+232x^230+188x^235+152x^240+72x^245+24x^250+12x^255+8x^260+4x^270

The gray image is a linear code over GF(5) with n=270, k=6 and d=195.
This code was found by Heurico 1.16 in 0.859 seconds.