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

generates a code of length 55 over Z2[X]/(X^2) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+25x^52+32x^54+59x^56+10x^60+1x^108

The gray image is a linear code over GF(2) with n=110, k=7 and d=52.
This code was found by Heurico 1.16 in 0.0383 seconds.