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.