The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  X  1  1  1  1  1 X^2  1 X^2  X  1  1
 0 X^3+X^2  0 X^3+X^2  0 X^3+X^2  0 X^2 X^3 X^3+X^2  0  0 X^3+X^2 X^3+X^2 X^3+X^2 X^3+X^2  0 X^3  0 X^3 X^3 X^3+X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^2  0
 0  0 X^3  0  0  0  0  0 X^3  0  0 X^3 X^3  0  0 X^3  0 X^3  0  0  0 X^3 X^3 X^3 X^3 X^3  0
 0  0  0 X^3  0  0  0 X^3  0  0  0  0  0 X^3  0 X^3 X^3 X^3 X^3 X^3  0 X^3  0 X^3 X^3  0  0
 0  0  0  0 X^3  0  0  0  0 X^3 X^3  0 X^3 X^3  0 X^3 X^3  0 X^3  0  0 X^3 X^3 X^3  0  0 X^3
 0  0  0  0  0 X^3  0 X^3  0 X^3 X^3 X^3  0  0  0 X^3 X^3  0  0  0 X^3  0 X^3  0 X^3 X^3  0
 0  0  0  0  0  0 X^3  0 X^3  0 X^3  0 X^3 X^3 X^3  0  0 X^3 X^3  0 X^3 X^3 X^3  0 X^3  0 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+64x^22+132x^24+192x^25+193x^26+896x^27+197x^28+192x^29+116x^30+51x^32+6x^34+2x^36+4x^38+1x^42+1x^44

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 0.046 seconds.