The generator matrix

 1  0  0  0  1  1  1  0  1  1  0  0  1  1  X  1  1  1  1  X  X  1  X  1  1  X  X  0  1  1  X  X  1  0  1  1  1  1  1  0  1  1  1  1  1  1  1  1  1  1  X  1  X  1
 0  1  0  0  X  1 X+1  1  0  1  1  X  0 X+1  1 X+1  0 X+1  X  X  1  1  1  X  X  0  X  1  1 X+1  1  1  0  1  1  0  1  X X+1  1  0  0  X  0 X+1  0  1  0 X+1  X  X  X  0  X
 0  0  1  0  0  0  0  X  1  1  1  1 X+1  1  X  X  X X+1 X+1  1  1 X+1 X+1  X X+1  1  X X+1  1  X  0  1  1 X+1  0 X+1  X  1  0  1  0  X  1 X+1  1  1 X+1  1 X+1  1  1 X+1  1  0
 0  0  0  1  1 X+1  X X+1 X+1  0  1 X+1  X  1  X X+1  1  1 X+1  X  0  1  0  X  0 X+1  1  0  X  0 X+1  1  1  X  1 X+1 X+1 X+1 X+1  X  X  X  X  0 X+1  X  0  0  0  0 X+1  X  1  1

generates a code of length 54 over Z2[X]/(X^2) who´s minimum homogenous weight is 50.

Homogenous weight enumerator: w(x)=1x^0+20x^50+38x^51+37x^52+52x^53+35x^54+12x^55+17x^56+8x^57+4x^58+10x^59+3x^60+4x^61+4x^62+4x^67+4x^68+1x^70+2x^72

The gray image is a linear code over GF(2) with n=108, k=8 and d=50.
This code was found by Heurico 1.16 in 0.0269 seconds.