The generator matrix
1 1 1 1 1 1 1 1 1 1 1 X X X^2 0 X 1 X 1 X 0 1
0 X 0 X 0 0 X X^2+X 0 X^2 X X^2 X X 0 X^2+X 0 X^2 0 X X 0
0 0 X X 0 X^2+X X 0 X^2 X X X X X^2+X X 0 0 X X^2+X X X^2 X^2
0 0 0 X^2 0 0 0 X^2 X^2 X^2 0 X^2 0 0 0 X^2 X^2 0 X^2 0 0 X^2
0 0 0 0 X^2 0 0 0 0 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 0 0
0 0 0 0 0 X^2 0 0 0 X^2 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 0 X^2 0
0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 0 0 0 0 X^2 0
generates a code of length 22 over Z2[X]/(X^3) who´s minimum homogenous weight is 16.
Homogenous weight enumerator: w(x)=1x^0+34x^16+56x^17+112x^18+160x^19+229x^20+296x^21+284x^22+304x^23+220x^24+152x^25+104x^26+48x^27+26x^28+8x^29+12x^30+1x^32+1x^36
The gray image is a linear code over GF(2) with n=88, k=11 and d=32.
This code was found by Heurico 1.16 in 0.0654 seconds.