The generator matrix

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

generates a code of length 58 over Z2[X]/(X^3) who´s minimum homogenous weight is 57.

Homogenous weight enumerator: w(x)=1x^0+72x^57+12x^58+16x^59+12x^60+4x^62+3x^64+8x^65

The gray image is a linear code over GF(2) with n=232, k=7 and d=114.
This code was found by Heurico 1.16 in 49.7 seconds.