The generator matrix

 1  0  1  1  1 X^2+X  1  1  0  1  1 X^2+X  1  1  1  1  0  1 X^2+X  1  1  1 X^2+X  0  1  1  1
 0  1 X+1 X^2+X  1  1  0 X+1  1 X^2+X X^2+1  1  0 X^2+X X^2 X+1  1 X^2+1  1 X^2+X X^2+1 X^2+X+1  1  1  0  0  0
 0  0 X^2  0  0  0  0 X^2  0 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0  0  0 X^2 X^2  0  0  0 X^2  0
 0  0  0 X^2  0  0 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2  0  0 X^2 X^2  0  0 X^2  0  0  0  0 X^2
 0  0  0  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2  0 X^2  0  0
 0  0  0  0  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2 X^2  0  0 X^2  0 X^2  0 X^2 X^2  0  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+22x^22+44x^23+63x^24+224x^25+48x^26+232x^27+46x^28+224x^29+48x^30+44x^31+15x^32+8x^34+2x^36+2x^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 0.0228 seconds.