The generator matrix

 1  0  0  1  1  1 X^2  1  1 X^2+X  X X^2  1 X^2+X  1 X^2  1 X^2  1  1  X  1  0  1  0 X^2+X  1
 0  1  0  0  1 X+1  1  1  X  X  1  1  X  1 X+1  1 X^2+X+1  0 X^2  1  X X^2+X  1  1  1 X^2  1
 0  0  1  1  1  0 X+1  X X^2+X+1  1 X^2+X  1  0 X+1 X^2+X  1 X+1  1  1  X  1  X  0 X+1 X^2+X+1  1 X+1
 0  0  0  X X^2+X X^2  X X^2  X  X  X  0 X^2+X X^2 X^2+X  X  0  X X^2 X^2+X  0  X X^2+X  0 X^2  X X^2+X
 0  0  0  0 X^2  0 X^2 X^2 X^2  0  0 X^2  0  0 X^2  0  0 X^2  0  0 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+110x^22+250x^23+378x^24+494x^25+514x^26+616x^27+602x^28+448x^29+322x^30+186x^31+101x^32+46x^33+14x^34+4x^35+6x^36+4x^37

The gray image is a linear code over GF(2) with n=108, k=12 and d=44.
This code was found by Heurico 1.16 in 0.228 seconds.