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  0  0  X  X  X  X  X  X  X  0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  X  0  0  0  0  0  X  X  0  X  X  0  0  X  X  X  X  0  0  0  0  X  X
 0  0  X  0  0  0  X  X  X  X  X  0  X  X  0  0  0  0  0  0  X  X  X  X  X  X  X  X  0  0  0  0  0  0  0  0  X  X  0  X  X  0  X  X  X  X  0  0  0  0  0  X  X  0
 0  0  0  X  0  X  X  X  0  0  0  0  X  X  X  X  0  0  X  X  X  X  0  0  0  0  X  X  X  X  0  0  0  0  X  X  X  0  X  X  X  0  0  0  0  X  X  0  0  0  X  X  0  0
 0  0  0  0  X  X  0  X  X  0  X  X  X  0  0  X  0  X  X  0  0  X  X  0  0  X  X  0  0  X  X  0  0  X  X  0  0  0  0  X  X  0  X  0  X  0  X  X  0  X  X  0  0  0

generates a code of length 54 over Z2[X]/(X^2) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+15x^52+32x^54+15x^56+1x^108

The gray image is a linear code over GF(2) with n=108, k=6 and d=52.
This code was found by Heurico 1.16 in 0.032 seconds.