The generator matrix

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

generates a code of length 54 over Z2[X]/(X^3) who´s minimum homogenous weight is 57.

Homogenous weight enumerator: w(x)=1x^0+10x^57+2x^58+2x^59+1x^60

The gray image is a linear code over GF(2) with n=216, k=4 and d=114.
As d=114 is an upper bound for linear (216,4,2)-codes, this code is optimal over Z2[X]/(X^3) for dimension 4.
This code was found by Heurico 1.16 in 0.055 seconds.