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

generates a code of length 56 over Z2[X]/(X^2) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+9x^52+16x^54+32x^55+15x^56+32x^57+12x^58+7x^60+3x^62+1x^110

The gray image is a linear code over GF(2) with n=112, k=7 and d=52.
This code was found by Heurico 1.16 in 0.0266 seconds.