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

generates a code of length 59 over Z2[X]/(X^3) who´s minimum homogenous weight is 58.

Homogenous weight enumerator: w(x)=1x^0+12x^58+96x^59+12x^60+3x^64+4x^70

The gray image is a linear code over GF(2) with n=236, k=7 and d=116.
This code was found by Heurico 1.16 in 0.0786 seconds.