The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  X  0  X X^2  1  X  1  1  1  1  X
 0  X  0  X  0  0  X X^2+X  0 X^2 X^2+X X^2  0  X  X  X X^2 X^2+X X^2  X  X X^2+X
 0  0  X  X  0 X^2+X  X  0 X^2  X  0  X  X  X  X  X  X  0  X X^2+X  X X^2
 0  0  0 X^2  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2
 0  0  0  0 X^2  0  0  0  0  0  0 X^2 X^2 X^2 X^2  0  0  0 X^2  0 X^2 X^2
 0  0  0  0  0 X^2  0  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0
 0  0  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2  0  0
 0  0  0  0  0  0  0 X^2  0  0  0  0 X^2 X^2  0 X^2  0 X^2 X^2 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+157x^16+240x^18+128x^19+693x^20+384x^21+880x^22+384x^23+710x^24+128x^25+272x^26+90x^28+16x^30+12x^32+1x^36

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 0.577 seconds.