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.