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

generates a code of length 60 over Z2[X]/(X^2) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+39x^56+176x^60+39x^64+1x^120

The gray image is a linear code over GF(2) with n=120, k=8 and d=56.
This code was found by Heurico 1.16 in 0.047 seconds.