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  X  X  1  X  X  X  X  X  X  0  X  0  X  0  X  0  0  0  0  0  X  X  X  X  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  0  0  X  0  0  X  X  X  X  X  0  0  X  X  X  X  X  0  0  0  0  X  X  0  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  X  X  0  0  0  X  0  X  0  0  X  X  0  0  X  X  X  X  0  0  X  X  0  0  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  X  X  X  X  0  0  0  0  0  0  X  X  0  X  0  0  X  X  X  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  0  X  X  X  0  0  X  X  0  0  X  X  X  X  X  X  0  0  0  X  0  0  0  X  X

generates a code of length 54 over Z2[X]/(X^2) who´s minimum homogenous weight is 53.

Homogenous weight enumerator: w(x)=1x^0+28x^53+14x^54+14x^56+4x^61+2x^62+1x^64

The gray image is a linear code over GF(2) with n=108, k=6 and d=53.
This code was found by Heurico 1.16 in 23.7 seconds.