The generator matrix

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

generates a code of length 16 over Z2[X]/(X^3) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+1x^16+12x^17+2x^18

The gray image is a linear code over GF(2) with n=64, k=4 and d=32.
As d=33 is an upper bound for linear (64,4,2)-codes, this code is optimal over Z2[X]/(X^3) for dimension 4.
This code was found by Heurico 1.16 in 0.000733 seconds.