The generator matrix
1 0 1 1 1 X^2 1 1 0 1 1 X 1 1 0 1 X 1 1 X^2+X X^2+X 1
0 1 1 0 X+1 1 1 0 1 X^2 X+1 1 X X^2+X+1 1 1 1 X^2+X 0 1 1 0
0 0 X 0 0 X^2 0 X^2+X X^2+X X^2+X X X^2 X^2 0 X X X^2 0 X^2+X X X^2 X
0 0 0 X X^2 X X^2+X X^2+X X^2+X X^2 X^2+X X^2+X X X^2+X X^2 X X^2 X^2 X X^2+X 0 X^2+X
generates a code of length 22 over Z2[X]/(X^3) who´s minimum homogenous weight is 18.
Homogenous weight enumerator: w(x)=1x^0+36x^18+96x^19+150x^20+172x^21+148x^22+162x^23+134x^24+64x^25+36x^26+12x^27+2x^28+4x^29+4x^30+2x^31+1x^32
The gray image is a linear code over GF(2) with n=88, k=10 and d=36.
This code was found by Heurico 1.16 in 0.0159 seconds.