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

generates a code of length 58 over Z2[X]/(X^2) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+93x^56+30x^64+3x^72+1x^80

The gray image is a linear code over GF(2) with n=116, k=7 and d=56.
This code was found by Heurico 1.16 in 10.1 seconds.