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

generates a code of length 58 over Z2[X]/(X^2) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+11x^54+14x^56+32x^57+15x^58+32x^59+12x^60+5x^62+5x^64+1x^114

The gray image is a linear code over GF(2) with n=116, k=7 and d=54.
This code was found by Heurico 1.16 in 0.016 seconds.