The generator matrix

 1  0  0  1  1  1  0  1  1  1  X  X  1  0  1  1  X  0  1  1  0  1  1  1  0  X  1  1  X  0  X  X  1  0  1  1  0  X  X  1  0  1  1  0  1  1  X  1  0  1  X  0  1  1  0  1  X  0
 0  1  0  0  1  1  1  0  X  1  0  1 X+1  1  X  X  1  X  1  1  1  X  1 X+1  1  0  1  0  1  1  1  1 X+1  X  X  X  1  X  1  1  1  1  1  1 X+1  X  1  X  0  0  1  1  0  1  1  1  0  1
 0  0  1  1  1  0  1  0  1 X+1  1  1  X  0 X+1  X X+1  1  1  X  0  X  1  0  X  1  0  X  1 X+1  X  X X+1  1 X+1 X+1  X  1 X+1  X X+1 X+1  X X+1 X+1 X+1 X+1  X  1  0 X+1  0  0  1  0  1  1 X+1
 0  0  0  X  0  0  0  0  0  X  X  0  0  X  X  X  0  X  0  0  X  X  0  0  0  X  X  0  0  X  0  X  X  X  0  X  0  0  0  X  X  X  0  0  0  X  X  X  0  X  X  0  0  0  0  X  0  X
 0  0  0  0  X  0  0  0  0  X  0  0  0  0  0  0  0  0  X  0  X  0  0  X  X  X  X  X  0  0  X  X  X  0  X  X  0  X  0  X  0  0  X  X  0  X  X  X  X  X  0  0  0  X  X  X  X  X
 0  0  0  0  0  X  0  0  X  X  X  0  X  X  0  X  0  X  0  X  0  X  X  0  X  0  X  X  X  0  0  X  0  0  X  0  0  0  X  0  X  X  X  X  X  0  0  X  0  0  0  X  0  0  X  0  X  0
 0  0  0  0  0  0  X  0  X  X  X  0  0  0  X  0  0  X  X  X  0  0  X  X  X  X  0  X  0  0  X  0  0  0  0  X  X  X  X  0  0  X  0  0  0  0  X  X  0  X  X  0  X  X  X  0  0  X
 0  0  0  0  0  0  0  X  0  0  0  0  X  0  0  0  X  X  X  0  X  X  X  X  X  0  0  0  0  0  X  X  0  X  X  0  X  0  X  X  X  X  0  X  0  0  X  0  X  X  0  X  0  0  0  X  X  0

generates a code of length 58 over Z2[X]/(X^2) who´s minimum homogenous weight is 50.

Homogenous weight enumerator: w(x)=1x^0+132x^50+271x^52+290x^54+280x^56+234x^58+231x^60+228x^62+169x^64+102x^66+63x^68+32x^70+6x^72+4x^74+3x^76+2x^78

The gray image is a linear code over GF(2) with n=116, k=11 and d=50.
This code was found by Heurico 1.16 in 8.72 seconds.