The generator matrix

 1  1  1  1  1  1  1  1  1  X  0  1  1  X  1  1  1  0  1  1  X  1
 0  X  0 X^2+X  0 X^2+X  0 X^2+X X^2 X^2+X  X  0 X^2+X X^2+X X^2+X X^2+X  0  X  0  X X^2  0
 0  0 X^2  0  0  0  0  0 X^2  0 X^2 X^2  0  0 X^2  0 X^2 X^2  0 X^2 X^2  0
 0  0  0 X^2  0  0  0 X^2  0  0 X^2 X^2 X^2 X^2  0  0 X^2  0  0 X^2 X^2  0
 0  0  0  0 X^2  0  0  0  0 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2  0 X^2 X^2  0
 0  0  0  0  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2  0  0  0  0 X^2 X^2  0 X^2  0
 0  0  0  0  0  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2 X^2  0  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+24x^16+18x^17+41x^18+44x^19+177x^20+62x^21+296x^22+72x^23+164x^24+46x^25+38x^26+12x^27+14x^28+2x^29+8x^30+3x^32+1x^34+1x^36

The gray image is a linear code over GF(2) with n=88, k=10 and d=32.
This code was found by Heurico 1.16 in 0.0209 seconds.