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

generates a code of length 57 over Z2[X]/(X^2) who´s minimum homogenous weight is 53.

Homogenous weight enumerator: w(x)=1x^0+12x^53+21x^54+24x^56+40x^57+12x^61+10x^62+7x^64+1x^102

The gray image is a linear code over GF(2) with n=114, k=7 and d=53.
This code was found by Heurico 1.16 in 0.062 seconds.