The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+6x^58+6x^60+2x^62+1x^64

The gray image is a linear code over GF(2) with n=112, k=4 and d=58.
This code was found by Heurico 1.16 in 0.045 seconds.