The generator matrix

 1  1  1  1  1  1  1  1  X  1  1  X  1  1  X  X X^2  0  X  X  1 X^2 X^3  1 X^2 X^2  1
 0 X^3+X^2 X^3 X^2  0 X^3+X^2 X^3 X^2 X^3+X^2  0 X^3+X^2 X^2 X^3 X^2  0 X^3 X^3+X^2 X^2 X^3+X^2 X^2  0 X^2 X^2 X^3 X^3  0  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+2x^26+48x^27+3x^28+8x^29+1x^30+1x^34

The gray image is a linear code over GF(2) with n=216, k=6 and d=104.
This code was found by Heurico 1.16 in 0.016 seconds.