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

generates a code of length 54 over Z5[X]/(X^2) who´s minimum homogenous weight is 205.

Homogenous weight enumerator: w(x)=1x^0+128x^205+160x^210+500x^212+132x^215+2000x^217+96x^220+28x^225+24x^230+8x^235+12x^240+12x^245+4x^250+16x^255+4x^265

The gray image is a linear code over GF(5) with n=270, k=5 and d=205.
This code was found by Heurico 1.16 in 0.0526 seconds.