The generator matrix

 1  0  1  1  1  X  1  1  0  1  1  X  1  1  1  1  0  X  1  1  1  1  0  X  1  1  1  1  0  X  1  1  1  1  X  X  0  0  X  X  X  0  1  1  1  1  0  X  X  X  0  1  1  1  1  1
 0  1 X+1  X  1  1  0 X+1  1  X  1  1  0 X+1  X  1  1  1  0  X X+1  1  1  1  0  X X+1  1  1  1  0  X X+1  1  0  X  X  1  1  0  X  X  0  X X+1  1  1  1  0  X  X  0  X X+1  1  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+2x^58+8x^59+3x^60+1x^62+1x^66

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 0.0514 seconds.