The generator matrix

 1  0  0  0  1  1  1  1 X^2  1  0  X  1  1 X^2+X  1  1  1 X^2  1  1 X^2  1  1 X^2+X X^2  1
 0  1  0  0  0  1 X^2 X^2+1  1 X+1 X^2+X  1 X^2+1  X  1 X^2+1 X^2  0  1 X+1 X^2+X+1 X^2 X^2+X  1  1  1  1
 0  0  1  0  0  1 X^2+1  X X^2+X+1 X^2+1  1 X^2 X^2+X  1 X+1 X^2 X^2+X  1  X X+1  1  1 X^2+X+1 X+1  X X^2+1 X^2+X+1
 0  0  0  1 X+1 X^2 X^2+X+1 X^2+1 X^2+1  1  1 X^2+1  X  0 X^2+X X^2 X^2+X+1 X^2+1  0  X X^2+X+1  X X^2+X+1 X^2+1 X^2+X+1 X^2+1 X^2+1
 0  0  0  0 X^2  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 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+365x^22+320x^23+892x^24+724x^25+1319x^26+1008x^27+1288x^28+696x^29+928x^30+304x^31+275x^32+20x^33+40x^34+8x^36+3x^38+1x^42

The gray image is a linear code over GF(2) with n=108, k=13 and d=44.
This code was found by Heurico 1.16 in 2.9 seconds.