The generator matrix

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

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+32x^16+62x^17+164x^18+302x^19+481x^20+662x^21+707x^22+662x^23+473x^24+298x^25+143x^26+58x^27+35x^28+2x^29+9x^30+2x^31+2x^32+1x^34

The gray image is a linear code over GF(2) with n=88, k=12 and d=32.
This code was found by Heurico 1.16 in 0.17 seconds.