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

generates a code of length 54 over Z5[X]/(X^2) who´s minimum homogenous weight is 185.

Homogenous weight enumerator: w(x)=1x^0+184x^185+752x^190+924x^195+1424x^200+3120x^205+11280x^210+27480x^215+27444x^220+1776x^225+1552x^230+1116x^235+668x^240+292x^245+84x^250+28x^255

The gray image is a linear code over GF(5) with n=270, k=7 and d=185.
This code was found by Heurico 1.16 in 20.8 seconds.