The generator matrix

 1  1  1  1  1  1  1  1  X  0  X  0  X  X  1  X  X  1  1 X^2 X^2  X
 0  X  0 X^2+X X^2 X^2+X X^2  X X^2+X  X X^2+X  X  0 X^2  0  X  X X^2  0  X  X X^2
 0  0 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2  0 X^2 X^2  0 X^2  0  0 X^2 X^2  0  0

generates a code of length 22 over Z2[X]/(X^3) who�s minimum homogenous weight is 21.

Homogenous weight enumerator: w(x)=1x^0+12x^21+39x^22+7x^24+4x^25+1x^30

The gray image is a linear code over GF(2) with n=88, k=6 and d=42.
This code was found by Heurico 1.16 in 0.0029 seconds.