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  X X^2  1  X  1  0  1  1  X  1  1 X^2  X  1  X  1 X^2  X  1  X  0  1
 0  X  0  0  0  X X^2+X  X X^2 X^2  X  0  0  X  X X^2+X  0  0 X^2+X  X X^2  X X^2+X  X X^2  0 X^2 X^2 X^2+X  0  X X^2+X  X X^2+X X^2+X  X  X  X  0 X^2+X X^2+X  X  X X^2+X X^2+X X^2 X^2+X  X  0 X^2+X  0  X  X  X  0  0 X^2 X^2
 0  0  X  0  X  X  X  0 X^2  0 X^2+X  X X^2+X  0 X^2+X  0 X^2 X^2+X X^2 X^2+X  0 X^2  X  0 X^2+X X^2+X  X X^2  X X^2  0 X^2+X  X  X  0 X^2 X^2+X  X X^2+X X^2  X X^2 X^2+X  X  0  0 X^2+X X^2+X  X X^2  0  X  0 X^2  0 X^2+X  X  0
 0  0  0  X  X  0  X X^2+X  0  X X^2  X X^2 X^2+X  X  0 X^2  X  X  0 X^2+X X^2 X^2+X X^2+X  0  0 X^2+X  X  X  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2+X X^2 X^2+X X^2 X^2+X X^2 X^2  X  0  0  X  0 X^2+X X^2 X^2+X X^2+X  X X^2 X^2  X
 0  0  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0  0  0 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0  0  0  0 X^2 X^2  0  0  0  0  0 X^2  0  0 X^2  0
 0  0  0  0  0 X^2  0 X^2  0  0  0 X^2 X^2  0 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0  0  0 X^2 X^2 X^2  0  0 X^2  0  0  0  0  0 X^2  0 X^2 X^2 X^2  0 X^2

generates a code of length 58 over Z2[X]/(X^3) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+275x^52+44x^53+180x^55+280x^56+288x^57+296x^59+221x^60+172x^61+36x^63+179x^64+8x^65+55x^68+12x^72+1x^92

The gray image is a linear code over GF(2) with n=232, k=11 and d=104.
This code was found by Heurico 1.16 in 21.7 seconds.