The generator matrix

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

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+142x^26+92x^28+16x^30+3x^32+2x^34

The gray image is a linear code over GF(2) with n=216, k=8 and d=104.
As d=107 is an upper bound for linear (216,8,2)-codes, this code is optimal over Z2[X]/(X^4) for dimension 8.
This code was found by Heurico 1.16 in 0.015 seconds.