The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  0  1 X^2  1  X  1  1  1  0  1  0  0  X
 0  X  0  X  0  0  X X^2+X X^2 X^2  X X^2+X  0 X^2  X X^2+X  X X^2+X X^2+X  X  X  X  0  0  0 X^2  0
 0  0  X  X  0 X^2+X  X X^2  0  X  X X^2+X X^2 X^2+X  0 X^2 X^2+X X^2  0  X X^2 X^2+X  X  0  X  X  0
 0  0  0 X^2  0  0 X^2  0  0  0  0  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0
 0  0  0  0 X^2  0  0  0 X^2 X^2  0 X^2 X^2 X^2  0 X^2  0  0  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2
 0  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  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+64x^22+8x^23+134x^24+64x^25+203x^26+112x^27+197x^28+64x^29+91x^30+8x^31+44x^32+25x^34+7x^36+1x^38+1x^40

The gray image is a linear code over GF(2) with n=108, k=10 and d=44.
This code was found by Heurico 1.16 in 0.0314 seconds.