The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  0  1  1  X X^3+X^2  1  1  X  X  1
 0  X X^3+X^2 X^2+X  0 X^2+X X^3+X^2 X^3+X X^3+X^2 X^2+X  0 X^3 X^3+X X^2+X X^3+X X^2+X  0  X  0 X^3 X^3+X  X X^3+X^2 X^3 X^2+X X^2+X  0
 0  0 X^3  0  0  0 X^3  0  0  0 X^3 X^3 X^3  0 X^3 X^3  0  0 X^3 X^3  0 X^3  0 X^3  0  0  0
 0  0  0 X^3  0  0 X^3  0 X^3 X^3 X^3 X^3 X^3 X^3  0 X^3  0 X^3  0  0  0  0  0 X^3  0  0 X^3
 0  0  0  0 X^3  0 X^3 X^3 X^3 X^3  0 X^3  0  0  0 X^3  0  0 X^3 X^3 X^3  0  0 X^3  0 X^3  0
 0  0  0  0  0 X^3 X^3  0 X^3 X^3  0  0 X^3  0 X^3 X^3 X^3  0  0 X^3  0 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 22.

Homogenous weight enumerator: w(x)=1x^0+26x^22+48x^23+93x^24+192x^25+525x^26+288x^27+521x^28+192x^29+84x^30+48x^31+22x^32+2x^34+3x^36+2x^38+1x^42

The gray image is a linear code over GF(2) with n=216, k=11 and d=88.
This code was found by Heurico 1.16 in 0.031 seconds.