The generator matrix

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

generates a code of length 58 over Z2[X]/(X^3) who´s minimum homogenous weight is 53.

Homogenous weight enumerator: w(x)=1x^0+134x^53+149x^54+306x^55+190x^56+308x^57+169x^58+186x^59+133x^60+166x^61+54x^62+88x^63+42x^64+54x^65+10x^66+22x^67+15x^68+8x^69+1x^70+6x^71+3x^72+2x^73+1x^74

The gray image is a linear code over GF(2) with n=232, k=11 and d=106.
This code was found by Heurico 1.16 in 0.219 seconds.