The generator matrix

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

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+58x^22+292x^23+408x^24+520x^25+602x^26+488x^27+522x^28+440x^29+342x^30+268x^31+107x^32+32x^33+6x^34+8x^35+2x^36

The gray image is a linear code over GF(2) with n=108, k=12 and d=44.
This code was found by Heurico 1.11 in 0.094 seconds.