The generator matrix
1 0 1 1 1 X^2 1 1 0 1 1 0 0 X 1 1 1 1 X 1 1 1 1 1 X 1 X
0 1 1 0 X+1 1 X^2+X+1 0 1 X^2 1 1 1 1 X+1 X X 1 1 X^2+X X+1 X+1 0 X 1 0 X^2
0 0 X 0 0 0 0 X^2+X X^2+X X^2+X X X^2+X X^2 X^2 X^2+X X X^2+X X^2 X 0 X^2 X 0 X^2 X^2+X X^2 0
0 0 0 X X^2 X^2+X X^2+X X^2+X X^2+X X^2 X 0 0 X^2+X X X^2 X^2+X X X X^2 0 0 X^2+X X X^2 X^2+X 0
generates a code of length 27 over Z2[X]/(X^3) who´s minimum homogenous weight is 24.
Homogenous weight enumerator: w(x)=1x^0+274x^24+232x^26+316x^28+144x^30+43x^32+8x^34+4x^36+2x^40
The gray image is a linear code over GF(2) with n=108, k=10 and d=48.
This code was found by Heurico 1.16 in 0.0911 seconds.