The generator matrix

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

generates a code of length 27 over Z2[X]/(X^3) who´s minimum homogenous weight is 23.

Homogenous weight enumerator: w(x)=1x^0+118x^23+262x^24+272x^25+280x^26+306x^27+246x^28+200x^29+168x^30+82x^31+65x^32+40x^33+6x^35+2x^36

The gray image is a linear code over GF(2) with n=108, k=11 and d=46.
This code was found by Heurico 1.11 in 0.125 seconds.