The generator matrix

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

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+120x^53+209x^54+254x^55+242x^56+210x^57+234x^58+148x^59+139x^60+146x^61+111x^62+70x^63+50x^64+44x^65+24x^66+22x^67+5x^68+6x^69+6x^70+3x^72+2x^73+2x^75

The gray image is a linear code over GF(2) with n=232, k=11 and d=106.
This code was found by Heurico 1.11 in 0.125 seconds.