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

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+10x^50+15x^52+32x^53+16x^54+32x^55+11x^56+5x^58+5x^60+1x^106

The gray image is a linear code over GF(2) with n=108, k=7 and d=50.
This code was found by Heurico 1.16 in 0.0354 seconds.