The generator matrix

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

generates a code of length 59 over Z2[X]/(X^3) who´s minimum homogenous weight is 60.

Homogenous weight enumerator: w(x)=1x^0+19x^60+4x^61+3x^62+4x^63+1x^66

The gray image is a linear code over GF(2) with n=236, k=5 and d=120.
As d=120 is an upper bound for linear (236,5,2)-codes, this code is optimal over Z2[X]/(X^3) for dimension 5.
This code was found by Heurico 1.16 in 0.0773 seconds.