The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^3+X  1  1 X^3+X^2  1  1 X^3+X^2  1  1 X^2+X  1  1 X^2  1  X  X  1 X^2  X
 0  1 X+1 X^2+X X^2+1  1 X^3+X^2 X^3+X^2+X+1  1 X^3+X X^3+1  1  0 X+1  1 X^3+X X^3+1  1 X^3 X^3+X+1  1 X^3+X^2+X X^3+X^2 X^3+X X^3+X^2+1  X  1
 0  0 X^3 X^3  0 X^3 X^3  0  0  0 X^3 X^3 X^3  0  0 X^3  0  0 X^3  0  0 X^3 X^3 X^3  0 X^3  0

generates a code of length 27 over Z2[X]/(X^4) who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+303x^26+156x^28+48x^30+3x^32+1x^42

The gray image is a linear code over GF(2) with n=216, k=9 and d=104.
As d=105 is an upper bound for linear (216,9,2)-codes, this code is optimal over Z2[X]/(X^4) for dimension 9.
This code was found by Heurico 1.16 in 118 seconds.