The generator matrix
1 0 1 1 1 X^2+X 1 1 0 1 1 X^2+X 1 1 0 1 1 X^2 1 1 1 1 X^2+X X 1 1 1
0 1 X+1 X^2+X X^2+1 1 0 X+1 1 X^2+X X^2+1 1 0 X+1 1 X^2+X X^2+X+1 1 X^2 X X^2+1 1 1 1 0 X^2 0
0 0 X^2 0 X^2 0 0 X^2 0 0 X^2 0 X^2 0 X^2 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 X^2 0
0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0 X^2 0 0 0 X^2 X^2 0 X^2 0 X^2 X^2 0 0 0 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+18x^24+80x^25+12x^26+32x^27+12x^28+80x^29+18x^30+1x^32+2x^38
The gray image is a linear code over GF(2) with n=108, k=8 and d=48.
This code was found by Heurico 1.16 in 0.00588 seconds.