The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  0  X  X  X
 0  X  0  0  0  X X^2+X  X  0 X^2 X^2 X^2 X^2  X X^2+X X^2+X X^2+X X^2  X  0  0 X^2+X
 0  0  X  0  X  X X^2+X  0  0  0 X^2+X  X X^2  X X^2  X X^2 X^2+X X^2+X  0 X^2 X^2
 0  0  0  X  X  0 X^2+X  X X^2 X^2+X  X  0 X^2 X^2 X^2+X  X  0 X^2+X X^2+X X^2+X  X X^2
 0  0  0  0 X^2  0  0  0 X^2  0  0 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2  0  0
 0  0  0  0  0 X^2  0 X^2  0  0 X^2 X^2  0  0 X^2 X^2  0  0  0 X^2  0 X^2
 0  0  0  0  0  0 X^2 X^2 X^2 X^2  0  0  0  0  0  0 X^2 X^2  0 X^2 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+134x^16+316x^18+64x^19+686x^20+448x^21+824x^22+448x^23+658x^24+64x^25+316x^26+114x^28+16x^30+7x^32

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 0.236 seconds.