The generator matrix

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

generates a code of length 27 over Z2[X]/(X^3) who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+152x^22+16x^23+218x^24+128x^25+444x^26+224x^27+367x^28+128x^29+192x^30+16x^31+109x^32+44x^34+8x^36+1x^44

The gray image is a linear code over GF(2) with n=108, k=11 and d=44.
This code was found by Heurico 1.16 in 0.601 seconds.