The generator matrix

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

generates a code of length 36 over Z2[X]/(X^3) who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+58x^36+2x^40+2x^44+1x^48

The gray image is a linear code over GF(2) with n=144, k=6 and d=72.
As d=72 is an upper bound for linear (144,6,2)-codes, this code is optimal over Z2[X]/(X^3) for dimension 6.
This code was found by Heurico 1.16 in 0.015 seconds.